Solve the absolute value equation 3|x+2|-7=14

Answer 1

To solve the absolute value equation 3|x+2|-7=14, we need to isolate the absolute value term and then solve for x.

Adding 7 to both sides of the equation, we get: 3|x+2|=21.

Dividing both sides of the equation by 3, we get: |x+2|=7.

Now we have two cases to consider with respect to the absolute value:

1) (x+2) = 7
Solving for x, we subtract 2 from both sides of the equation: x = 7 - 2 = 5.

2) -(x+2) = 7
Solving for x, we first distribute the negative sign: -x - 2 = 7.
Then, we add 2 to both sides of the equation: -x = 7 + 2 = 9.
Finally, we multiply both sides of the equation by -1 to solve for x: x = -9.

Therefore, the solutions to the absolute value equation 3|x+2|-7=14 are x = 5 and x = -9.