Question

How do you solve `7|x+2|=49`?

Answer 1

Isolate the absolute value term and then solve for + and - of what it is equal to. See Explanation for full detailed process.

Explanation:

First step is to isolate the absolute value term by dividing each side of the equation by `color(red)(7)` which will also keep the equation balanced.

`(7abs(x + 2))/color(red)(7) = 49/color(red)(7)`

`(color(red)(cancel(color(black)(7)))abs(x + 2))/cancel(color(red)(7)) = 7`

`abs(x + 2) = 7`

Because the absolute value function transforms a negative or positive term into a positive term we must solve for the term in the absolute value function for both its positive and negative equivalent.

Solution 1)

`x + 2 = 7`

`x + 2 - color(red)(2) = 7 - color(red)(2)`

`x + 0 = 5`

`x = 5`

Solution 2)

`x + 2 = -7`

`x + 2 - color(red)(2) = -7 - color(red)(2)`

`x + 0 = -9`

`x = -9`