# Absolute Value Equations 1

#### 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

##### Administrator
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$$\displaystyle | x + 5| = 15$$

$$\displaystyle (x + 5) = 15$$

$$\displaystyle x + 5 = 15$$

$$\displaystyle x + 5 - 5 = 15 - 5$$

$$\displaystyle x = 10$$

Check

$$\displaystyle |(10) + 5| = 15$$

$$\displaystyle |15| = 15$$

Negative side:

$$\displaystyle | x + 5| = 15$$

$$\displaystyle -(x + 5) = 15$$

$$\displaystyle -x - 5 = 15$$

$$\displaystyle -x - 5 + 5 = 15 + 5$$

$$\displaystyle -x = 20$$

$$\displaystyle \dfrac{x}{-1} = \dfrac{20}{-1}$$

$$\displaystyle x = -20$$

Check

$$\displaystyle |(-20) + 5| = 15$$

$$\displaystyle |-15| = 15$$

Two solutions of $$\displaystyle 10, -20$$

Last edited:
• harpazo

#### MarkFL

##### La Villa Strangiato
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Administrator
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Math Helper
When I see:

$$\displaystyle |x+5|=15$$

This says to me "find all the numbers on the number line whose distance from -5 is 15."

$$\displaystyle x=-5\pm15\implies x\in\{-20,10\}$$

• harpazo and anemone

Banned
Good work, guys.