One Step Inequalities Worksheet, Word Problems, and Definition
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Key Points about One Step Equations
One-step inequalities are fundamental algebraic concepts involving a single operation and variable. Solving them requires understanding basic arithmetic, algebraic properties, and inequalities. Mastering one-step inequalities is crucial for progressing to more complex equations.
Solving one-step inequalities involves isolating the variable by performing opposite operations on both sides of the inequality. Addition/subtraction and multiplication/division are the main operations used. Remember to flip the inequality sign when multiplying/dividing by a negative number.
One-step inequalities have practical applications in real-world situations like budgeting, planning, and data analysis. Proficiency in solving one-step inequalities is essential for success in algebra and beyond.
How to Solve One Step Inequalities
One Step Inequalities are inequalities that take only one step to solve. This means that you only have to add, subtract, multiply, or divide one time in order to solve the inequality. Each One Step Inequality will use one of the four basic operations of math and only one. You can tell when an expression is an inequality by looking at the math symbol in the middle of the expression.
One-step inequalities are a fundamental concept in algebra that every student must learn. They are a type of algebraic equation that involves only one operation and one variable. Solving one-step inequalities requires students to use their knowledge of basic arithmetic, algebraic properties, and inequalities. Once students master one-step inequalities, they can move on to more complex algebraic equations.
To solve one-step inequalities, students must isolate the variable on one side of the equation. They can do this by performing the same operation on both sides of the equation. For example, if the inequality is 3x + 5 > 8, students can subtract 5 from both sides of the equation to get 3x > 3. Then, they can divide both sides by 3 to get x > 1. This process involves understanding the order of operations, the properties of inequalities, and the basic algebraic skills of simplifying expressions.
If the expression has a greater than, less than, greater than or equal to, or less than or equal to symbol in the expression then the expression is an inequality. One Step Inequalities can be solved by adding once, subtracting once, multiplying once, or dividing once. If you multiply or divide the inequality by a negative number, then the inequality sign must change directions.
One-step inequalities are an essential part of algebra and are used in many real-world situations, such as budgeting, planning, and data analysis. It is important for students to master one-step inequalities to be successful in algebra and beyond.
Common Core Standard: 7.EE.1
Related Topics: Combining Like Terms, Distributive Property, Two Step Equations, Two Step Inequalities, Multi Step Inequalities
Return To: Home, 7th Grade
Solving One Step Inequalities
When solving one-step inequalities, there are two main operations that are used: addition/subtraction and multiplication/division. By using these operations, it is possible to isolate the variable and solve for its possible values.
Addition and Subtraction
To solve an inequality that involves addition or subtraction, the goal is to isolate the variable on one side of the inequality. This is done by performing the opposite operation on both sides of the inequality. For example, if the inequality is x + 3 < 7, you would subtract 3 from both sides to get x < 4.
It is important to remember that when adding or subtracting a negative number, the direction of the inequality must be flipped. For example, if the inequality is x - 5 > -2, you would add 5 to both sides to get x > 3.
Multiplication and Division
To solve an inequality that involves multiplication or division, the goal is to isolate the variable on one side of the inequality. This is done by performing the opposite operation on both sides of the inequality. For example, if the inequality is 2x > 10, you would divide both sides by 2 to get x > 5.
It is important to remember that when multiplying or dividing by a negative number, the direction of the inequality must be flipped. For example, if the inequality is -3x < 12, you would divide both sides by -3, but also flip the direction of the inequality to get x > -4.
In summary, when solving one-step inequalities, it is important to isolate the variable by performing opposite operations on both sides of the inequality. By doing so, it is possible to determine the range of values that the variable can take.
One Step Inequalities Definition
One-step inequalities are mathematical expressions that compare two values and determine the relationship between them. They are called one-step inequalities because they can be solved using only one arithmetic operation.
Inequalities are similar to equations, but instead of an equal sign, they use inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). The inequality symbol indicates the relationship between the values being compared.
One-step inequalities are used to represent real-world situations where there are constraints or limitations. For example, if a person needs to save at least $50 per week to reach a savings goal, they can use a one-step inequality to represent this constraint.
To solve a one-step inequality, the goal is to isolate the variable on one side of the inequality symbol. This is done by performing the same arithmetic operation on both sides of the inequality. The solution is the set of values that make the inequality true.
One-step inequalities are foundational concepts in algebra and are used in many applications, including finance, engineering, and science.
The Secret to Solving One Step Inequalities Examples
- Determine if you must add, subtract, multiply, or divide to solve the Inequality.
- Remember that you have to “undo” what is being done in the inequality.
- If you have to multiply or divide by a negative number then the sign of the inequality symbol changes directions.
One-step inequalities are a type of algebraic inequality that can be solved in a single step. They are a fundamental concept in algebra and are essential for solving more complex equations. In this section, we will look at some examples of one-step inequalities and how to solve them.
Example 1: x + 5 < 10
To solve this inequality, we need to isolate the variable x on one side of the equation. We can do this by subtracting 5 from both sides of the equation:
x + 5 – 5 < 10 – 5
x < 5
The solution to this inequality is x < 5, which means that any value of x that is less than 5 will satisfy the inequality.
Example 2: 3y – 2 > 7
To solve this inequality, we need to isolate the variable y on one side of the equation. We can do this by adding 2 to both sides of the equation:
3y – 2 + 2 > 7 + 2
3y > 9
Next, we divide both sides of the equation by 3:
3y/3 > 9/3
y > 3
The solution to this inequality is y > 3, which means that any value of y that is greater than 3 will satisfy the inequality.
Example 3: -4z ≤ 16
To solve this inequality, we need to isolate the variable z on one side of the equation. Since the inequality is less than or equal to, we can solve it by dividing both sides of the equation by -4. However, we need to remember that when we divide by a negative number, we need to flip the inequality sign:
-4z/(-4) ≥ 16/(-4)
z ≤ -4
The solution to this inequality is z ≤ -4, which means that any value of z that is less than or equal to -4 will satisfy the inequality.
Overall, these examples demonstrate how to solve one-step inequalities by isolating the variable on one side of the equation. It is important to remember to flip the inequality sign when dividing by a negative number.
5 Quick One Step Inequalities Practice Problems
Graphing One Step Inequalities
Graphing one-step inequalities is a straightforward process that involves plotting points on a coordinate plane. A one-step inequality is an inequality that can be solved in a single step. These inequalities involve just one variable and one single operation, such as addition, subtraction, multiplication, or division.
To graph a one-step inequality, you need to determine the solution set of the inequality and then plot the points that satisfy the inequality on a coordinate plane. The solution set of an inequality is the set of all values of the variable that make the inequality true.
For example, consider the inequality x + 2 < 5. To solve this inequality, you need to subtract 2 from both sides to isolate x. This gives you x < 3, which is the solution set of the inequality. To graph this inequality, you need to plot all the points on the number line that are less than 3.
To graph the inequality on a coordinate plane, you need to draw a line that represents the boundary of the solution set. In this case, the boundary is a vertical line that passes through x = 3. You should draw a dashed line to indicate that the points on the line are not included in the solution set.
Next, you need to shade the region that satisfies the inequality. Since the inequality is x < 3, you need to shade the region to the left of the boundary line. This is because all the points to the left of the line have x values that are less than 3, which satisfies the inequality.
In summary, graphing one-step inequalities involves determining the solution set of the inequality, plotting the points that satisfy the inequality on a coordinate plane, drawing a dashed line to represent the boundary, and shading the region that satisfies the inequality.
One Step Inequalities Word Problems
One-step inequalities can be used to solve real-life problems. These types of problems are common in many fields, including finance, engineering, and science. In this section, we will explore some examples of one-step inequality word problems.
Example 1: Money Management
Suppose a person has a monthly income of $2000 and wants to save at least $500 per month. They also have monthly expenses of $1200. How much money can they spend each month on discretionary items like entertainment and dining out?
To solve this problem, we can use a one-step inequality. Let x be the amount of money they can spend on discretionary items. Then, we have:
2000 - 1200 - x >= 500
Simplifying this inequality, we get:
x <= 300
Therefore, the person can spend at most $300 per month on discretionary items.
Example 2: Temperature Control
A factory needs to keep its temperature between 20°C and 25°C to prevent damage to its products. If the temperature is currently at 18°C, how much can it increase before it becomes too high?
To solve this problem, we can use a one-step inequality. Let x be the amount by which the temperature can increase. Then, we have:
18 + x <= 25
Simplifying this inequality, we get:
x <= 7
Therefore, the temperature can increase by at most 7°C before it becomes too high.
Example 3: Weight Loss
A person wants to lose at least 5 pounds per month. They currently weigh 180 pounds. How much can they weigh at the end of 6 months if they follow their weight loss plan?
To solve this problem, we can use a one-step inequality. Let x be the amount of weight they can lose in 6 months. Then, we have:
180 - 5x <= ?
We don’t know the upper bound of this inequality, but we do know that they want to lose at least 5 pounds per month for 6 months. Therefore, we have:
180 - 5(6) <= ?
Simplifying this inequality, we get:
150 <= ?
Therefore, they can weigh at most 150 pounds at the end of 6 months if they follow their weight loss plan.
These examples demonstrate how one-step inequalities can be used to solve real-life problems. By setting up an inequality and solving it, we can find the maximum or minimum value of a variable that satisfies a given condition.
Common Mistakes in Solving One Step Inequalities
When solving one-step inequalities, there are several common mistakes that people tend to make. These mistakes can lead to incorrect answers and a lack of understanding of the concept. In this section, we will discuss some of the most common mistakes made when solving one-step inequalities.
Mistake #1: Forgetting to Flip the Inequality Sign
One of the most common mistakes made when solving one-step inequalities is forgetting to flip the inequality sign when multiplying or dividing by a negative number. For example, if you have the inequality 2x > -6 and you divide both sides by -2, you need to remember to flip the inequality sign, resulting in x < 3. Failure to do so can result in an incorrect answer.
Mistake #2: Incorrectly Distributing Negative Signs
Another common mistake is incorrectly distributing negative signs when solving one-step inequalities. For example, if you have the inequality -3x < 9 and you divide both sides by -3, you need to remember to distribute the negative sign to both sides of the inequality, resulting in x > -3. Failure to do so can result in an incorrect answer.
Mistake #3: Not Simplifying the Answer
It is important to simplify the answer when solving one-step inequalities. For example, if you have the inequality 4x + 8 > 20 and you subtract 8 from both sides, you need to simplify the answer by dividing both sides by 4, resulting in x > 3. Failure to simplify the answer can result in an incorrect answer.
Mistake #4: Misunderstanding the Concept of Inequalities
Finally, one of the most common mistakes made when solving one-step inequalities is a lack of understanding of the concept of inequalities. It is important to remember that an inequality represents a range of values, not just a single value. For example, if you have the inequality 2x + 1 < 7, the solution is x < 3, which represents a range of values from negative infinity to 3. Failure to understand this concept can result in an incorrect answer.
In conclusion, when solving one-step inequalities, it is important to avoid common mistakes such as forgetting to flip the inequality sign, incorrectly distributing negative signs, not simplifying the answer, and misunderstanding the concept of inequalities. By being aware of these mistakes and taking steps to avoid them, you can improve your understanding of one-step inequalities and achieve more accurate results.
How to Solve One Step Equations FAQ
How do I solve one-step inequalities on a number line?
To solve one-step inequalities on a number line, you need to represent the inequality on the number line and then identify the solutions. The solutions are all the values that make the inequality true. You can use the same rules for solving one-step inequalities as you would for solving one-step equations.
What are two-step inequalities?
Two-step inequalities are inequalities that require two steps to solve. These inequalities involve two operations, such as addition and multiplication or subtraction and division.
How do you solve one-step inequalities by adding or subtracting?
To solve one-step inequalities by adding or subtracting, you need to isolate the variable on one side of the inequality. You can do this by adding or subtracting the same value to both sides of the inequality. Just remember to reverse the inequality symbol if you multiply or divide by a negative number.
What is the process for solving one-step inequalities using multiplication and division?
To solve one-step inequalities using multiplication and division, you need to isolate the variable on one side of the inequality. You can do this by multiplying or dividing both sides of the inequality by the same value. Just remember to reverse the inequality symbol if you multiply or divide by a negative number.
How do you solve one-step inequalities with fractions?
To solve one-step inequalities with fractions, you need to isolate the variable on one side of the inequality. You can do this by multiplying or dividing both sides of the inequality by the reciprocal of the fraction. Just remember to reverse the inequality symbol if you multiply or divide by a negative fraction.
What are the steps to solve one-step equations?
The steps to solve one-step equations are:
- Isolate the variable on one side of the equation.
- Perform inverse operations to undo the operations on the variable.
- Simplify both sides of the equation.
What is the definition of one-step inequalities?
One-step inequalities are inequalities that can be solved in one step. These inequalities involve only one operation, such as addition, subtraction, multiplication, or division.
What are the rules for inequalities?
The rules for inequalities are:
- If you add or subtract the same value from both sides of an inequality, the inequality remains true.
- If you multiply or divide both sides of an inequality by a positive value, the inequality remains true.
- If you multiply or divide both sides of an inequality by a negative value, the inequality must be reversed to remain true.
One Step Inequalities Worksheet Video Explanation
Watch our free video on how to solve 1 step inequalities. This video shows how to solve problems that are on our free solving One Step Inequalities worksheet that you can get by submitting your email above.
Watch the free One Step Inequalities video on YouTube here: One Step Inequality Video
Video Transcript:
This video is about how to solve one step inequalities you can get the one step inequality worksheet used in this video for free by clicking on the link in the description below. You will learn exactly what is a one step inequality and the one step inequalities definition. Solving one step inequalities is very similar to solving equations except there are a couple extra steps and things you need to remember. Now an equation will always have an equal sign separating two sides of the equation inequalities can have one of four different types of symbols.
Inequalities could have a less than symbol, less than or equal to, greater than, and greater than or equal to. Now for the most part solving one step inequalities is about the same as solving equations with one important difference. For example, in this inequality x plus 4 is less than or equal to 4. You would still solve it the same way that you would solve a regular equation. You would try to isolate the x by getting it on one side by itself. In order to do this in this example you have to get rid of this plus 4. The opposite of plus four is to subtract four.
The fours on this side will cancel. You’re left with just x on this side and you have your less than or equal to symbol in the middle. And then four minus four is zero. Our answer is going to be x is less than or equal to zero and then you can graph it on the number line. We’re going to put our bracket in and then we’re going to have our arrow, which is pointing in the same direction, go to the left.
The biggest difference in solving one step inequalities from equations is that when you divide or multiply by a negative number the sign will change. For example, in this problem we have negative x is greater than or equal to negative 9. In order to isolate this x, we have to make it positive.
What we’re going to do is we’re going to divide or multiply but, in this case, we’re going to divide both sides by negative 1. The reason we divide by negative 1 is so that the negatives cancel and you’re left with just positive x on this side. But because you divided by a negative the symbol in the middle, the greater than or equal to symbol, will change into a less than or equal to symbol.
Then negative 9 divided by negative 1 becomes positive 9. Your answer is going to be x is less than or equal to positive 9. Now when we graph this one, we go to 9 on the number line, we put in a bracket because it’s equal to, and then it goes to the left because it’s less than 9.
Let’s do a couple practice problems on our one-step inequalities worksheet. Our first problem gives us x plus 3 is less than 10. We have to solve for x by getting x on one side of the inequality by itself. In order to do that I’m going to draw my line down the middle. I know that everything I do to one side of this inequality I also have to do the other. The first step is in order to get x by itself, we have to get rid of this plus three.
We’re going to subtract three from this side, that way they cancel and then because we did it to this side of the inequality, we also have to do it to this side. We do 10 minus 3 on this side. We bring down our x, we bring down our less than symbol, which has not changed, and then we bring down 10 minus 3, which is seven. The solution is x is less than seven. We’re going to put a parenthesis on this seven and then we’re going to draw our line to the left because we know that our solution is everything that is less than seven.
Number two on our one step inequalities worksheet gives us 5x is greater than negative 35. Again, we have to get x by itself. We’re going to start with drawing our line. 5x is greater than negative 35. This is like saying 5 times x and the opposite of 5 times something is to divide by 5. We divide this side by 5 because we want the 5’s to cancel. Whatever you do to one side of the inequality you also have to do the other so we also divide this side by 5.
This side we have x the 5’s are canceled and we just have x is greater than and then negative 35 divided by 5 five is negative seven. Now when we go to graph this, we have x is greater than negative seven. We go to negative seven which is right here, we draw a parenthesis and then we draw the arrow in the direction that the sign is pointing. Greater than would be everything in this direction.
The last problem we’re going to complete on our one step equalities worksheet is number eight. Number eight gives us negative 3x is greater than 15. We draw our line. We know everything that we do on this side of the inequality we also have to do the other side. We have negative 3x is greater than 15. This is like saying negative 3 times x so we have to get rid of this negative 3 times x.
The opposite of negative three times something is to divide by negative three. We divide by negative three on this side so that the threes and the negatives cancel. Whatever you do to one side you also have to do the other. We’re going to divide by negative three on this side. We’re left with x on the left on this side and then we divided by a negative number. This is a negative number so our symbol in the middle is going to change.
It goes from greater than to less than because we divide it by negative and then 15 divided by negative 3 is negative 5. The solution is x is less than negative 5. We go to negative 5 on our number line, we draw a parenthesis and then we go to the left because that’s the way our symbol points. Try all of the practice problems by downloading the free solving one-step inequalities worksheets above.
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