The Best Method for Solving Multi Step Inequalities

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Here’s how to Solve Multi Step Inequalities

Solving Multi Step Inequalities is when a linear inequality has multiple Like Terms on the same side of the inequality symbol. The first thing you must do is realize that Like Terms exist on the same side of the inequality symbol. Once you have recognized that the inequality has Like Terms on the same side, you combine them by either adding them together or subtracting them. After you Combine the Like Terms, you solve the inequality just like any other Two Step Inequality. The first step in solving Two Step Inequalities is to get all of the constants (numbers) on one side of the inequality symbol, and the coefficient with the variable on the other side. In order to do this you must use the addition and subtraction property of equality to get the constants on the opposite side as the variable. Once the constants are separated from the variable, you must use the multiplication or division property of equality to cancel out the coefficient on the variable. You can always check your answer by substituting your solution back in to the inequality for the variable. If you multiply or divide by a negative number when solving your Multi Step Inequality you must change the direction of the inequality symbol.

Common Core Standard: 7.EE.1

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The Complete answer to “What are Multi Step Inequalities?”

Here is the guide to learn how to do multi step inequalities: Simplifying Multi Step Inequalities is what you do when you have Like Terms on a similar side of the inequality symbol. When you have recognized that the inequality has Like Terms on a similar side, you join them by either adding them together or subtracting them. After you Combine the Like Terms, you simplify the inequality like some other Two Step Inequality. The first in comprehending Two Step Inequalities is to get the majority of the constants (numbers) on one side of the inequality symbol, and the coefficient with the variable on the opposite side. When the constants are isolated from the variable, you will divide everything by the coefficient on the variable. You can generally check your answer by substituting your answer back in to the inequality for the variable. In the event that you multiply or divide by a negative number when simplifying your Multi Step Inequality you should change the direction of the symbol.

4 Easy Steps for Solving any Multi Step Inequalities Example

Combine Like terms that are on the same side of the inequality by adding them together or subtracting them from each other.
Add or subtract the constants so that you get the variable and constant on opposite side of the inequality.
Divide the entire inequality by the coefficient on the variable to solve the inequality.
If you multiplied or divided by a negative number you have to change the direction of the inequality symbol.

Solving Multi Step Inequalities Practice Problems Quiz

Watch the Video Explanation of our Multi Step Inequalities Worksheet

Watch our free video on how to solve Multi Step Inequalities. This video shows how to solve problems that are on our free solving Multi Step Inequalities worksheet that you can get by submitting your email above.

Watch the free Multi Step Inequalities video on YouTube here: Multi Step Inequalities Video

Video Transcript:

This video is about solving multi-step inequalities. You can get the multi-step inequalities worksheet used in this video for free by clicking on the link in the description below. Solving any multi step inequalities examples is very similar when solving for multi step equations. You will combine like terms, you’ll solve for the variable, and then if you divide by a negative number it’s going to change the direction of the symbol of your inequality. This first example problem gives us negative 3x minus 5 plus 6x is less than or equal to 46. The first step in this multi step inequality is to combine like terms. If you combine negative 3x plus 6x you get positive 3x. You bring down your minus 5, bring down your less than or equal to symbol, and the 46. The next step is to get x by itself. We’re going to add 5 to this side and to this side. The 5’s cancel and we’re left with 3x is less than or equal to 51. Then the final step is to divide both sides by 3 so that you get x by itself on this side. These threes will cancel and then 51 divided by 3 is 17. The solution is x is less than or equal to 17. Let’s do a couple practice problems on our multi step inequalities worksheet.

The first problem we’re going to do on our multistep inequalities worksheet is number one. The problem gives us 1 plus 4x plus 3 is greater than 20. The first thing we need to do is we need to combine like terms. In this case we’re going to add 1 plus 3 because they are the like terms on the left side of the inequality and 1 plus 3 is 4. We bring down the 4x and then we combine 1 and 3. We bring down our greater than symbol and then 20. Then the next step is we have to get x by itself. We’re going to subtract 4 from both sides so that this 4 cancels and we’re left with 4x is greater than 20 minus 4 is 16. The last step is we have to get rid of this 4x. This is like saying 4 times x. The opposite of that is to divide by 4. These fours cancel and we’re left with x is greater than 16, divided by four is four. The solution is x is greater than four.

The next problem we’re going to do on the solve multi step inequalities worksheet is number six. This problem gives us 10x plus three plus 4x is greater than or equal to negative 25. Again, the first step is to combine like terms. We combine 10x plus 4x and we get 14x. Bring down the plus 3 and the greater than symbol and the negative 25. Then we have to get x on one side by itself. We’re going to subtract 3 from this side so that the 3s cancel, whatever you do to one side you also have to do the other. We subtract 3 on this side and we bring down our 14x is greater than or equal to negative 25. Minus 3 is negative 28. And then 14 times x we have to undo. We divide both sides by 14. The 14s cancel we’re left with just x on this side is greater than or equal to negative 28 divided by 14 is negative two. Our answer is x is greater than or equal to negative two.

Finally, the last problem on our multi step inequalities worksheet is going to be number seven. We have negative x plus one minus x is less than or equal to negative 77. Again, the first step is to combine like terms. We have negative x and this is like negative 1x minus another negative 1x. Negative 1 minus 1 is negative 2. We have negative 2x, bring down our plus 1, our less than or equal to symbol, and our negative 77. Then we have to get x on one side by itself. We’re going to subtract 1 here so that the ones cancel. We do minus 1 here so now we have negative 2x is less than or equal to negative 77 minus 1 is negative 78. Then we have to undo this negative 2x. This is like negative 2 times x so we divide by negative 2 so that the negatives and the 2s cancel. Whatever you do to one side you do the other. You divide this side by negative 2 as well. We have x on this side, now we divided by a negative number and because we divided by a negative it’s going to change our symbol from less than or equal to, to greater than or equal to. Now we have x is greater than or equal to and then negative 78 divided by negative 2 is positive 39. The solution is x is greater than or equal to 39.