Question

How do you solve the equation `|x + 3| + 10 = 4`?

Answer 1

An absolute value can either be positive or negative on the inside, so we will end up with two solutions. However, we must beware of extraneous solutions, solutions that do not work in the original equation. It is for this reason that we must check our solutions in the original equation at the end.

Explanation:

`|x + 3| = -6`

Let's start with the positive scenario.

`x + 3 = -6`

`x = -9`

Now, we do the negative. You must make the absolute value a parentheses, so that you can distribute the negative.

`-(x + 3) = -6`

`-x - 3 = -6`

`-x = -3`

`x = 3`

However, when we check both solutions in the original equation we notice neither works. This means that the equation has no solution `{O/}`

Practice exercises:

1. Solve for x.

a) `|2x + 3| = 3`

b) `4x + 7 = |x - 4|`

Challenge problem

Solve for x in `|2x - 7| = |3x + 11|`

Good luck!