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

1 Answer
Mar 7, 2016

Answer:

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!