Solve the Absolute Value Equation: 2|x - 4| = 10

2x4=10 2|x - 4| = 10

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1

Understand the problem

2x4=10 2|x - 4| = 10

2

Step-by-step solution

To solve the equation 2x4=10 2|x - 4| = 10 , divide both sides by 2. This gives x4=5|x - 4| = 5 .

The absolute value equation x4=5|x - 4| = 5 implies that x4=5x - 4 = 5 or x4=5x - 4 = -5 . Solving these equations:

1. x4=5x - 4 = 5 gives x=9x = 9 .

2. x4=5x - 4 = -5 gives x=1x = -1 .

Thus, the solutions are x=9x = 9 and x=1x = -1 .

3

Final Answer

Answers b + c

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\( \left|x\right|=3 \)

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