Solve 2|x + 2| − 6 = 18
Absolute value equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = −14, x = 10 |
Step-by-step solution
8 steps-
1 Given2 \left|{x + 2}\right| - 6 = 18
Solve for x.
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2 Isolate the absolute value\left|{x + 2}\right| = 12
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3 Split into two cases: the expression inside the bars is either 12 or -12
|u| is the distance of u from 0. A distance of 12 can be on either side of 0, so the inside is 12 or the opposite of 12, and each case is solved as its own equation.
x + 2 = 12\quad \text{or} \quad x + 2 = -12 -
4 Case 1x + 2 = 12
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5 Subtract 2 from both sides
An equation stays true as long as you do the same thing to both sides, like adding the same weight to both pans of a balance. Adding or subtracting the same amount on both sides moves a term to the other side, where it appears with the opposite sign.
x = 10Move the constant terms to the right.
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6 Case 2x + 2 = -12
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7 Subtract 2 from both sidesx = -14
Move the constant terms to the right.
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8 Check\begin{aligned}x = -14:\quad 18 = 18\quad\checkmark\\ x = 10:\quad 18 = 18\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| −14 | 18 | 18 | ✓ |
| 10 | 18 | 18 | ✓ |
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