Question

How do you solve `|10x + 2| - 18 = -12`?

Answer 1

This is an absolute value equation. As a result, we must consider two scenarios: that the absolute value is positive or negative.

Explanation:

First, before I solve the equation, let me prove the point I made above to further your understanding.

Let's look at an extremely simple equation involving absolute value.

`|x| = 2`

An absolute value, by definition, means the distance on the number line between 0 and the number. This distance doesn't take into account direction and therefore always is positive.

So, we must consider in the above equation the following:

x = 2 or -x = 2

x = 2 or x = -2

Checking these solutions back in the equation, you'll notice both will work, since `|-2| = 2`

Solving your equation:

We must first isolate the absolute value:

`|10x + 2| = 6`

`10x + 2 = 6 or -(10x + 2) = 6`

`10x = 4 or -10x - 2 = 6`

`x = 2/5 or -4/5`

Hopefully this helps, and happy voting tomorrow!