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Mathematics
London Maxwell
18 October, 02:18
Absolute value equation |x-3|=5
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Tamara Hughes
18 October, 03:40
0
8
Step-by-step explanation:
x-3=5
=x=5+3
x=8
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Lizbeth Banks
18 October, 05:28
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x = - 2, x = 8
Step-by-step explanation:
The absolute value function always returns a positive value, but the expression inside can be positive or negative, thus
x - 3 = 5 OR - (x - 3) = 5
Solving both equations
x - 3 = 5 (add 3 to both sides)
x = 8
OR
- x + 3 = 5 (subtract 3 from both sides)
- x = 2 (multiply both sides by - 1)
x = - 2
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are solutions.
x = 8
| 8 - 3 | = | 5 | = 5 = right side
x = - 2
| - 2 - 3 | = | - 5 | = 5 = right side
Thus the solutions are x = - 2, x = 8
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