Question

Solve for x: −3|x + 7| = −12

a. x = 5/3, x = -19/3
b. x = -3, x = -11
c. x = -3, x = 11
d. No solution

Answer 1

To solve −3|x + 7| = −12, we divide both sides by −3 to get |x + 7| = 4. Then we create two equations: x + 7 = 4 and x + 7 = −4. Solving these gives us x = −3 and x = −11.

Step-by-step explanation:

To solve the equation −3|x + 7| = −12, let's first isolate the absolute value expression by dividing both sides of the equation by −3:

|x + 7| = 4

Now, knowing that the absolute value of a number can be either positive or negative, this gives us two equations to solve:

1. x + 7 = 4
2. x + 7 = −4

Solving the first equation:

x + 7 = 4
x = 4 − 7
x = −3

Solving the second equation:

x + 7 = −4
x = −4 − 7
x = −11

So the solutions are x = −3 and x = −11, which corresponds to option b.