Math  /  Algebra

QuestionWhat are the solution(s) to the equation 2x7=15|2 x-7|=15 x=4x=4 x=11x=11 x=4x=-4 x=2x=2

Studdy Solution

STEP 1

1. The equation involves an absolute value, 2x7=15 |2x - 7| = 15 .
2. The absolute value equation can have two possible cases: one where the expression inside is positive and one where it is negative.

STEP 2

1. Set up the two cases for the absolute value equation.
2. Solve each case for x x .
3. Verify which solutions are valid from the given options.

STEP 3

The absolute value equation 2x7=15 |2x - 7| = 15 can be split into two separate equations:
Case 1: 2x7=15 2x - 7 = 15
Case 2: 2x7=15 2x - 7 = -15

STEP 4

Solve Case 1: 2x7=15 2x - 7 = 15
Add 7 to both sides:
2x7+7=15+7 2x - 7 + 7 = 15 + 7 2x=22 2x = 22
Divide both sides by 2:
x=222 x = \frac{22}{2} x=11 x = 11

STEP 5

Solve Case 2: 2x7=15 2x - 7 = -15
Add 7 to both sides:
2x7+7=15+7 2x - 7 + 7 = -15 + 7 2x=8 2x = -8
Divide both sides by 2:
x=82 x = \frac{-8}{2} x=4 x = -4

STEP 6

Verify which solutions are valid from the given options:
The solutions we found are x=11 x = 11 and x=4 x = -4 .
Given options: - x=4 x = 4 - x=11 x = 11 - x=4 x = -4 - x=2 x = 2
The valid solutions from the options are x=11 x = 11 and x=4 x = -4 .
The solution(s) to the equation are:
x=11andx=4 x = 11 \quad \text{and} \quad x = -4

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