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Video: Solving Linear Inequalities with a Variable on Each Side

Kathryn Kingham

Solve the following inequality: 9𝑦 > 77 + 2𝑦.

01:47

Video Transcript

Solve the inequality nine 𝑦 is greater than 77 plus two 𝑦.

When our instructions tell us to solve the following inequality, what they’re asking us to do is find the values for 𝑦 that make the statement true. To do that, we’ll need to isolate 𝑦. Right now, we have a 𝑦 on both sides of our inequality. Before we can isolate 𝑦, we’ll need to get both of these variables onto the same side of the equation.

We can do that by subtracting two 𝑦 from both sides of our inequality. Nine 𝑦 minus two 𝑦 equals seven 𝑦. Bring down our inequality symbol. Bring down the 77. Two 𝑦 minus two 𝑦 equals zero. So there’s nothing to bring down there. In this line, seven is being multiplied by 𝑦. But we want 𝑦 by itself. So we can divide seven 𝑦 by seven and also 77 by seven. Seven 𝑦 divided by seven equals 𝑦. Bring down our inequality symbol. 77 divided by seven equals 11.

This is our solution to the inequality. Nine is greater than eleven. Any time we plug in something larger than eleven for 𝑦 in this inequality, this statement will be true. 𝑦 is greater than eleven.