Video: Solving One-Step Linear Inequalities

If 𝑥 − 8 > −3, then 𝑥 > _.

01:46

Video Transcript

If 𝑥 minus eight is greater than negative three, then 𝑥 is greater than blank.

Okay, so to find the missing value, what we’re gonna have to do is to solve this inequality here. We’re gonna solve the inequality in the same way that we’d solve an equation. So we’re actually gonna use the same method.

So first of all, we’re actually going to add eight to each side. And we actually get our answer, which is 𝑥 is greater than five. We get that because if we’ve added eight to the left-hand side, that’s 𝑥 minus eight plus eight, so they’ll cancel each other out, that equal zero. So it’s 𝑥 on its own. And then on the right-hand side, negative three plus eight is five, making sure that actually you’re counting to right- you’re counting up from negative three, not down because a common mistake here might be the answer of negative 11.

So therefore, we can say that if 𝑥 minus eight is greater than negative three, then 𝑥 is going to be greater than five. We can quickly check our answer with a couple of values of 𝑥. So I’ve got 𝑥 equals six and 𝑥 equals five. So if I look at the left-hand side first, if I substitute 𝑥 is equal to six into our top inequality, you get six minus eight, which is equal to negative two. And this is greater than negative three. So yes, great! This would fit, so- so that this would be a suitable solution for 𝑥.

However, if we look on the right-hand side where 𝑥 is equal to five, if you substitute that in, we get five minus eight, which would give us an answer of negative three. Well, negative three is actually not greater than negative three. So yes, they’ve both agreed with our solution. So, say, yeah, we’re confident that 𝑥 is greater than five.

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