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Penny
Mathematics
12 December, 00:23
Solve for |2x + 4|-1=7
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Ezra Mckee
12 December, 00:41
0
x = - 6 or x = 2
Step-by-step explanation:
The absolute value function always returns a positive value. However, the expression inside can be positive or negative.
Given
| 2x + 4 | - 1 = 7 (add 1 to both sides)
| 2x + 4 | = 8, thus
2x + 4 = 8 (subtract 4 from both sides)
2x = 4 (divide both sides by 2)
x = 2
OR
- (2x + 4) = 8
- 2x - 4 = 8 (add 4 to both sides)
- 2x = 12 (divide both sides by - 2)
x = - 6
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 2 → | 4 + 4 | - 1 = | 8 | - 1 = 8 - 1 = 7 ← True
x = - 6 → | - 12 + 4 | - 1 = | - 8 | - 1 = 8 - 1 = 7 ← True
Hence the solutions are x = - 6 or x = 2
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