# Absolute Value Equations 2

#### harpazo

##### Pure Mathematics
Banned
Let's go back to high school together as we explore the world of absolute value equations. Ready to have fun with math?

#### TheJason

Staff member
Moderator
$$\displaystyle | x - 10| = 100$$

$$\displaystyle (x - 10) = 100$$

$$\displaystyle x - 10 = 100$$

$$\displaystyle x - 10 + 10 = 100 + 10$$

$$\displaystyle x = 110$$

Check

$$\displaystyle |(110) - 10| = 100$$

$$\displaystyle |100| = 100$$

Negative side:

$$\displaystyle | x - 10| = 100$$

$$\displaystyle -(x - 10) = 100$$

$$\displaystyle -x + 10 = 100$$

$$\displaystyle -x + 10 - 10 = 100 - 10$$

$$\displaystyle -x = 90$$

$$\displaystyle \dfrac{x}{-1} = \dfrac{90}{-1}$$

$$\displaystyle x = -90$$

Check

$$\displaystyle |(-90) - 10| = 100$$

$$\displaystyle |-100| = 100$$

Two solutions of $$\displaystyle 110,-90$$

harpazo

#### harpazo

##### Pure Mathematics
Banned
$$\displaystyle | x - 10| = 100$$

$$\displaystyle (x - 10) = 100$$

$$\displaystyle x - 10 = 100$$

$$\displaystyle x - 10 + 10 = 100 + 10$$

$$\displaystyle x = 110$$

Check

$$\displaystyle |(110) - 10| = 100$$

$$\displaystyle |100| = 100$$

Negative side:

$$\displaystyle | x - 10| = 100$$

$$\displaystyle -(x - 10) = 100$$

$$\displaystyle -x + 10 = 100$$

$$\displaystyle -x + 10 - 10 = 100 - 10$$

$$\displaystyle -x = 90$$

$$\displaystyle \dfrac{x}{-1} = \dfrac{90}{-1}$$

$$\displaystyle x = -90$$

Check

$$\displaystyle |(-90) - 10| = 100$$

$$\displaystyle |-100| = 100$$

Two solutions of $$\displaystyle 110,-90$$
Hope you like your journey back to Algebra 1.