Question

You need to reverse the symbol to solve which inequality?

Answer 1

When you multiply/divide by a negative number while solving the inequality, you reverse the symbol.

A.)  4(5 - y) ≥ 80       To solve this, isolate/get the variable "y" by itself in the inequality. Divide 4 on both sides

$\frac{4(5-y)}{4} \geq \frac{80}{4}$

5 - y ≥ 20       Subtract 5 on both sides

5 - 5 - y ≥ 20 - 5

-y ≥ 15     Divide -1 on both sides to get "y" by itself

$\frac{-y}{-1} \geq \frac{15}{-1}$       Because you are dividing by a negative number, you need to reverse the sign

y ≤ -15

B.) 2(y - 3) ≥ 8      Isolate "y", divide 2 on both sides

y - 3 ≥ 4      Add 3 on both sides to get "y" by itself

y ≥ 7

C.) 3y - 4 > 1       Add 4 on both sides

3y > 1       Divide 3 on both sides to get "y" by itself

$y>\frac{1}{3}$

D.) $-\frac{3}{4} +6y > \frac{1}{4}$       Isolate "y", add 3/4 on both sides

6y > 1     Divide 6 on both sides to get "y" by itseld

$y>\frac{1}{6}$