Solve for x: Understanding the Absolute Value in |x + 4| = 10

∣x+4∣=10 \left|x+4\right|=10

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1

Understand the problem

∣x+4∣=10 \left|x+4\right|=10

2

Step-by-step solution

To solve the equation ∣x+4∣=10 \left|x+4\right|=10 , we split it into two separate equations:

1. x+4=10 x+4=10

2. x+4=−10 x+4=-10

For the first equation:

x+4=10 x+4=10

Subtract 4 from both sides:

x=6 x=6

For the second equation:

x+4=−10 x+4=-10

Subtract 4 from both sides:

x=−14 x=-14

Thus, the solutions are x=6 x=6 and x=−14 x=-14 .

3

Final Answer

x=6 x=6 , x=−14 x=-14

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

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