Solve 2|x − 9| − 1 = 17
Absolute value equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = 0, x = 18 |
Step-by-step solution
8 steps-
1 Given2 \left|{x - 9}\right| - 1 = 17
Solve for x.
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2 Isolate the absolute value\left|{x - 9}\right| = 9
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3 Split into two cases: the expression inside the bars is either 9 or -9
|u| is the distance of u from 0. A distance of 9 can be on either side of 0, so the inside is 9 or the opposite of 9, and each case is solved as its own equation.
x - 9 = 9\quad \text{or} \quad x - 9 = -9 -
4 Case 1x - 9 = 9
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5 Add 9 to 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 = 18Move the constant terms to the right.
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6 Case 2x - 9 = -9
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7 Add 9 to both sidesx = 0
Move the constant terms to the right.
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8 Check\begin{aligned}x = 0:\quad 17 = 17\quad\checkmark\\ x = 18:\quad 17 = 17\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 0 | 17 | 17 | ✓ |
| 18 | 17 | 17 | ✓ |
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