Video: Solving One-Step Linear Inequalities

Solve the following inequality: −2 ≥ 𝑥/0.8.

02:03

Video Transcript

Solve the following inequality. Negative two is greater than or equal to 𝑥 over 0.8. In this inequality, on the left, we have negative two. And that value must be greater than or equal to 𝑥 over 0.8. Another way to show that would be 𝑥 divided by 0.8.

Our goal is to solve this inequality. We need to find a value or values that make the inequality true. And to do that, we’ll need to isolate 𝑥. Because on the right we have 𝑥 divided by something, to get 𝑥 by itself, we need the reciprocal. We need to do the opposite. The opposite of divide by 0.8 is multiply by 0.8. And if we multiply the right-hand side by 0.8, we need to multiply the left-hand side by 0.8. 0.8 times negative two is negative 1.6.

Now 𝑥 divided by 0.8 multiplied by 0.8 would be equal to 𝑥 times one. Divide by 0.8 multiplied by 0.8 equals one. And 𝑥 times one just equals 𝑥. So we bring down our inequality symbol. And we see that negative 1.6 is greater than or equal to 𝑥.

However, this is not a very common way to write inequalities. If we want to flip this around, we can put the 𝑥 on the left. But in order to do that, we’ll need to flip the sign. One way to check is to see if the tip of the arrow is pointing in the same direction. It was pointing at the 𝑥. So it should remain pointing at the 𝑥. And then bring down the negative 1.6. It is completely true to say negative 1.6 is greater than or equal to 𝑥. But the more common notation is 𝑥 is less than or equal to negative 1.6.

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