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
[tex]\frac{4(5-y)}{4} \geq \frac{80}{4}[/tex]
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
[tex]\frac{-y}{-1} \geq \frac{15}{-1}[/tex] 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
[tex]y>\frac{1}{3}[/tex]
D.) [tex]-\frac{3}{4} +6y > \frac{1}{4}[/tex] Isolate "y", add 3/4 on both sides
6y > 1 Divide 6 on both sides to get "y" by itseld
[tex]y>\frac{1}{6}[/tex]
