Question

Solve the absolute value equation. Check your solutions.

| 5x + 13| = –7

Answer 1

x=-2

Answer 2

There will be two separate equations to solve from:
First when the 5x+13 is positive which means x>-13/5
which leads to
+(5x+13)=-7 solving it gives the value as -4
since we 've assumed the above eqn for case x>-13/5 thus -4 is discarded.

Now another eqn comes when 5x+13 is -ve means x<-13/5
which leads to
-(5x+13)=-7 which gives us a solution as x=-6/5 which is discarded because previously we 'd assumed it for x<-13/5 but -6/5 is greater than -13/5

Hence there is no solution to this equation.
We can prove it by graphically also.
.