# Welcome to Algebra I: Solving Multistep Linear Inequalities Algebraically

14 minutes

(female describer) 4 times x plus 1 minus 9x is less than 54.

(teacher) Okay, let's first use the distributive property so we can get this cleaned up a bit. So, 4 times x--4x-- 4 times 1--plus 4-- minus 9x-- going to bring everything else down--less than 54. We have like terms on the left side we combine: the 4x and the negative 9x. You combine 4x and negative 9x. That's negative 5x plus 4, less than 54. Okay. Going to keep moving along. Scroll down a little bit. I'm trying to isolate that negative 5x, so let's subtract 4 from both sides. Bring down our negative 5x, is less than 54 minus 4. That's 50. Give me a little more room here. Okay, we're at the last step to get x by itself. We need to divide both sides by negative 5. This is going to cancel, and we have x. Remember that property of inequality. If we divide both sides by a negative number, we flip that inequality sign-- changes the relationship. 50 divided by 5, that's negative 10. My solution set-- have my brace-- x colon x is greater than negative 10. This is, "x such that x is greater than negative 10." We got through that one. And I do believe it's your turn to try. Press pause. Take your time and work through these. When you're ready to compare your answers, press play.

(female describer) Represent each solution set using set-builder notation. 1. 2/3x minus 1 is less than or equal to 5. 2. 5x plus 4 is greater than 7x plus 10.

(teacher) Okay, let's see how you did. Let's get these little answer hiders out of the way. For number one, you should have got x such that x is less than or equal to 9. For number 2, x such that x is less than 3. Let me show you how I got those, in case you need to see. We're going to start out-- make sure I've got the pen. We'll isolate that 2/3, so I start by adding 1 to both sides. Plus 1, plus 1, so cancel that right there. Bring down my 2/3x, less than or equal to-- 5 plus 1 is 6. I treat this fraction like it's a division problem. So 2 divided by 3-- the opposite of dividing by 3 is to multiply by 3. I'm going to multiply both sides by 3. On the left side, cancel those 3s out and I'm just left with 2x, less than or equal to 6 times 3. That's 18. Little more workspace. Then for our last step, divide both sides by 2, so x is less than or equal to-- 18 divided by 2 is 9. If we represented that in set-builder notation-- got our brace-- x such that x is less than or equal to 9, okay? Let's try the other one. So, want to isolate x. I'm going to start by subtracting 7x from both sides. That cancels on the right. 5x minus 7x, that's negative 2x plus 4 greater than 10. Next step's going to be to subtract 4 from both sides. So, minus 4, minus 4. All right. So, negative 2x, greater than-- 10 minus 4 is 6. Final step-- divide by negative 2. Because we're dividing both sides by a negative, we've got to flip that inequality sign. 6 divided by 2 is negative 3. If we wrote that using set-builder notation-- let's get a little more space underneath-- brace, x such that x is less than negative 3. Now just before I let you go, another way you see set-builder notation-- instead of a colon, you may see just a bar, like, "x such that x is less than negative 3." That's another way you may see the set-builder notation, okay? Great job, guys. Now you're familiar with how to solve multi-step linear inequalities algebraically. Hope to see you for more Algebra I. Bye. Accessibility provided by the U.S. Department of Education.

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In this program students learn that solving multistep inequalities is very similar to solving simple equations. The rules for solving inequalities include maintaining the balance of the equation. Part of the "Welcome to Algebra I" series.

## Media Details

Runtime: 14 minutes