|x+7| = 9

a. x = 2, x = -16
b. x = 2, x = -2
c. x = 0, x = 9
d. no solution

a

Step-by-step explanation:

The absolute value function always gives a positive result, however, the expression inside can be positive or negative, thus

x + 7 = 9 or - (x + 7) = 9

Solve both equations

x + 7 = 9 ( subtract 7 from both sides )

x = 2

OR

-(x + 7) = 9, that is

- x - 7 = 9 ( add 7 to both sides )

- x = 16 ( multiply both sides by - 1 )

x = - 16

Solutions are x = 2, x = - 16 → a

b.

step-by-step explanation: