Question Video: Solving One-Step Linear Inequalities

Rewrite 𝑥/6 < −2 so that only 𝑥 appears on the left-hand side.

01:41

Video Transcript

Rewrite 𝑥 over six is less than negative two so that only 𝑥 appears on the left-hand side.

We have 𝑥 over six is less than negative two. Before we go any further, it’s really helpful for us to think about how we multiply and divide inequalities. When we’re multiplying or dividing with positives, the signs stay the same. And we do the same operation to both sides. When we’re multiplying or dividing with negatives, the sign is flipped. And we multiply or divide by the same thing on either side.

We’re trying to get 𝑥 by itself on the left-hand side. Currently, on the left, there is 𝑥 divided by six. And to get rid of 𝑥 divided by six, we need to multiply by six. Six is a positive value, which means our sign won’t change. But we’ll still need to multiply by the same amount on both sides. 𝑥 divided by six times six equals 𝑥. And negative two times six equals negative 12. And so we see that 𝑥 is less than negative 12.

If we wanted to graph that on our number line, we would have an open circle. And the arrow would go to the left. If we want to check if this is true, we can plug in a value that is less than negative 12 into the original inequality. I’m gonna choose negative 18. I know that negative 18 is less than negative 12, and it’s divisible by six. Negative 18 divided by six is negative three. And it is true that negative three is less than negative two, which confirms 𝑥 is less than negative 12.

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