Could someone please help me with this math problem?

Question

Solve using the multiplication principle. Give the answer in set-builder notation.
-4/5 less than or equal to -8x.
I want to say that I multiply both sides by 5 but I'm not sure. I'm confused with this problem.
Thanks.

Answer 1

you are trying to solve for x. How does multiplying by 5 do that? Why not start by multiplying by 1/8? You do have one more step.

Answer 2

go with your instinct

-4/5 ≤ -8x
times by +5
-4 ≤ -8x
"move" the terms
8x ≤ 4
divide by 8
x ≤ 1/2

remember you switch the inequality sign only if you multiply or divide the inequation by a negative, we multiplied by +8, so it stayed the same.

Answer 3

forgot to multiply the right side by 5

-4 ≤ -40x
40x ≤ 4
x ≤ 1/10

Answer 4

Thanks.