Solve the absolute value equation.-7(y + 5) < -9y - 35

Step 1
Solve the absolute value function as follows.
${\displaystyle -7(y+5)<-9y-35}$
${\displaystyle -7\cdot y+(-7)\cdot 5<-9y-35}$ (Multiply -7 inside the paranth eses)
${\displaystyle -7y-35<-9y-35}$
${\displaystyle -7y-35+35<-9y-35+35}$ (Add 35 to both sides)
${\displaystyle -7y<-9y}$
Step 2
On further simplification.
${\displaystyle -7y+9y<-9y+9y}$ (Add 9y to both sides)
${\displaystyle 2y<0}$
${\displaystyle \frac{2y}{2}<\frac{0}{2}}$ (Divide the inequality by 2 on both sides)
${\displaystyle y<0}$
Step 3
Result:
The solution set of the absolute value function is ${\displaystyle \left\{y\mid y<0\right\}}$ or using interval notation, ${\displaystyle (-\propto ,0)}$.