Could someone please help me with this math problem?

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.

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.

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.

forgot to multiply the right side by 5

-4 ≤ -40x
40x ≤ 4
x ≤ 1/10

Thanks.

Sure! I'll be happy to help you with this math problem.

To solve the inequality "-4/5 less than or equal to -8x," you can use the multiplication principle. The multiplication principle states that if you multiply both sides of an inequality by the same positive number, the inequality remains unchanged. However, if you multiply both sides of an inequality by the same negative number, the inequality direction is flipped.

In this case, you want to isolate the variable x. To do that, you can start by multiplying both sides of the inequality by -5. However, since you're multiplying by a negative number, you need to flip the direction of the inequality.

Here's the step-by-step process:

Step 1: Start with the inequality: -4/5 ≤ -8x
Step 2: Multiply both sides of the inequality by -5: (-5)(-4/5) ≥ (-5)(-8x)
Simplify: 4 ≥ 40x
Step 3: Divide both sides of the inequality by 40 to isolate x: (4/40) ≥ (40x/40)
Simplify: 1/10 ≥ x
Step 4: Rewrite the inequality in set-builder notation: x ∈ {x | x ≤ 1/10}

So, the answer in set-builder notation for the inequality -4/5 ≤ -8x is x ∈ {x | x ≤ 1/10}.