Question

Please help, I'm stuck on this answer.

True or false? Explain your answer.
The inequality −2(x + 10) ≥ 75 says the same thing as −2x − 20 ≥ 75. I can multiply by -2 on the left side without reversing the inequality symbol.

Answer 1

Answer:True

Explanation:

Yes, you don't have to reverse the inequality symbol since the variables are not from the other side (right).

Answer 2

I agree with what that person told you. The expression -2(x+10) is equivalent to -2x-20

Multiply the outer -2 with the inner x to get -2 times x = -2x

Multiply the outer -2 with the inner term 10 to get -2 times 10 = -20

So overall, -2(x+10) = -2x-20

--------------------------------------------

So that's how we're able to go from this
`-2(x+10) \ge 75` to this
`-2x-20 \ge 75`

The only thing that changes is the left side. The inequality sign will not flip. It only flips if we multiply both sides by a negative number.