Video: Writing and Solving Linear Inequalities

Write an inequality to describe the following, and then solve it: Negative five times a number is at least −45.

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Video Transcript

Write an inequality to describe the following and then solve it. Negative five times a number is at least negative 45.

We’ll start by writing the inequality. We’ve got negative five being multiplied by some number, which we’ll represent with the variable 𝑥, at least negative 45. We know the other side will have a negative 45. But what symbol should “at least” represent?

We need to consider if this could be more, equal, or less. “At least” means it could be equal, but it could not be less. “At least” could also mean more. So it’s equal to or more than. And mathematically, we would represent that with a greater than or equal to symbol. If negative five times a number is at least negative 45, then negative five 𝑥 is greater than or equal to negative 45.

This is the first part of the problem, but we’ll now need to try and solve for 𝑥. Since we’re dealing with an inequality, it should immediately be on our radar that if we’re multiplying and dividing with positive values, the sign stays the same. But if we’re multiplying or dividing with a negative number, we have to flip the sign. 𝑥 is being multiplied by negative five. And to get 𝑥 by itself, to solve for 𝑥, we’ll need to divide both sides of the equation by negative five. Since we are dividing by a negative here, we must flip the inequality symbol. Negative five 𝑥 divided by negative five equals 𝑥. The sign is flipped. And negative 45 divided by negative five is nine. Negative five 𝑥 is greater than or equal to negative 45. And that means 𝑥 is less than or equal to nine.

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