Question

How do you solve `4 + abs(r + 2 ) =7`?

Answer 1

First subtract `4` from both sides to get: `abs(r+2) = 3`

So either `r+2 = 3`, giving `r = 1`

or `r+2 = -3`, giving `r = -5`

Explanation:

Let's look at the definition of absolution value first:

`abs(x) = x` if `x > 0`

`abs(x) = 0` if `x = 0`

`abs(x) = -x` if `x < 0`

So if `abs(x) = a`, then `a >= 0` and `x = +-a`

Now subtract `4` from both sides of our original equation to get:

`abs(r+2) = 3`

From what we have found, `r+2 = +-3`

Subtract `2` from both sides to get:

`r = -2 +- 3`

That is `r = -5` or `r = 1`