3 Easy Tricks for Solving One Step Inequalities

Here’s how to Solve One Step Inequalities

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The complete answer to “What are one Step Inequalities?”

Are you wondering how to do one step inequalities? Then check out the quick guide below.

One Step Inequalities refers to inequalities that make just a single step to simplify. Every One Step Inequality needs just one of the four basic arithmetic functions of math to solve. You just need to add, subtract, multiply, or divide one time to solve. If the symbol in the middle of the expression is a inequality symbol then the expression is an inequality. It could be have a greater than, greater than or equal to, less than, or less than or equal to symbol. If you have to multiply or divide by a negative number then the sign of your inequality symbol will change directions.

3 Easy Steps for Solving One Step Inequalities Examples

1. Determine if you must add, subtract, multiply, or divide to solve the Inequality.
2. Remember that you have to “undo” what is being done in the inequality.
3. If you have to multiply or divide by a negative number then the sign of the inequality symbol changes directions.

 

Solving One Step Inequalities Practice Problems Quiz

Watch the short Video on our One Step Inequalities Worksheet

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.