Absolute Value Equations 1

harpazo

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

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TheJason

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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 \(\displaystyle 10, -20\)
 
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MarkFL

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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."

\(\displaystyle x=-5\pm15\implies x\in\{-20,10\}\)
 
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harpazo

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Good work, guys.