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Video: Solving One-Step Linear Inequalities

Bethani Gasparine

If a+46≥39, then _.

01:29

Video Transcript

If 𝑎 plus forty-six is greater than or equal to thirty-nine, then blank.

Here we can solve this inequality for 𝑎. In order to do that, we need to subtract forty-six from both sides of the inequality. On the left side, the forty-six cancels. And on the right-hand side, thirty-nine minus forty-six is negative seven. So 𝑎 is greater than or equal to negative seven.

Let’s go ahead and make sense of this first. So if eight plus forty-six is greater than or equal to thirty-nine, we found that numbers greater than or equal to negative seven will hold true for this inequality.

So since our answer was 𝑎 is greater than or equal to negative seven, that means we can plug in negative seven or greater than negative seven. So negative seven plus forty-six is thirty-nine. Thirty-nine is greater than or equal to thirty-nine because it’s actually equal to thirty-nine. So if we’ve plugged in numbers that were bigger than negative seven, we wouldn’t get an answer that’s bigger than thirty-nine. And that’s okay. Say it was forty. Forty is greater than or equal to thirty-nine. So if 𝑎 plus forty-six is greater than or equal to thirty-nine, then 𝑎 is greater than or equal to negative seven.