Question

You need to reverse the symbol to solve which inequality?

A) 4(5-y) greater than or equal to 80
B) 2(y-3) greater than or equal to 8
C) 3y - 4, >1
D -3/4 + 6y > 1/4

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

`(4(5-y))/(4) \geq (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

`(-y)/(-1) \geq (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>(1)/(3)`

D.)
`-(3)/(4) +6y > (1)/(4)` Isolate "y", add 3/4 on both sides

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

`y>(1)/(6)`