Question

Solve for x: −4|x + 5| = −16

Answer 1

`-4|x+5|=-16 \\ |x+5|=(-16)/(-4) \\ |x+5|=4 \\ x+5=4 \ \lor \ x+5=-4 \\ x=4-5 \ \lor \ x=-4-5 \\ x=-1 \ \lor \ x=-9 \\ \boxed{x=-1 \hbox{ or } x=-9}`

Answer 2

`x_(1)` = -1 and
`x_(2)` = -9

Explanation:

1. Write the equation to solve:

−4|x + 5| = −16

2. Pass the -4 to divide the -16

|x + 5| =
`(-16)/(-4)`

|x + 5| = 4

3. As you have an absolute value you should solve to equations, that is:

x+5 = 4 (Eq.1)

-x-5 = 4 (Eq. 2)

4. Solve Eq. 1:

x+5 = 4

x = 4-5

x = -1

5. Solve Eq. 2:

-x-5 = 4

x = -5 - 4

x = -9

Therefore the x values are:
`x_(1)` = -1 and
`x_(2)` = -9