# Do you flip the inequality sign when distributing 2 different negative numbers on both sides?

I can't figure out whether I should flip the sign or not.

Problem:

-2(0.5-4s) ≥ -3(4-3.5s)

-1+8s ≤ -12+10.5s

11+8s ≤ 10.5s

11 ≤ 2.5s

4.4 ≤ s

Is this correct or does the greater than sign stay the same?

Relevance

No:

1) you should NEVER flip the direction of an inequality. Multiplying (or dividing) by a negative requires this, but you can avoid it by simply switching sides and thus flipping the inequality.

2) you ONLY flip the direction when you actually multiply both sides by a negative (or divide by a negative).

You didn't multiply both sides by a negative, you just have a negative on both sides:

-2(0.5 - 4s) ≥ -3(4 - 3.5s)

-->

-1 + 8s ≥ -12 + 10.5s

--> subtract 8s from both sides, add 12 to both sides

11 ≥ 2.5s

--> divide by 2.5, multiply by 2/5

4.4 ≥ s --> s ≤ 4.4

• The greater than sign remains the same. Because here you did not multiply the sides of

the inequality through by a negative number, what you did is simply expand the expressions

on both sides of the inequality. This does NOT reverse the sign of the inequality.