Solve the Absolute Value Equation: |2x+3| = 9

∣2x+3∣=9 \left|2x+3\right|=9

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1

Understand the problem

∣2x+3∣=9 \left|2x+3\right|=9

2

Step-by-step solution

To solve the equation ∣2x+3∣=9 \left|2x+3\right|=9 , we split it into two separate equations:

1. 2x+3=9 2x+3=9

2. 2x+3=−9 2x+3=-9

For the first equation:

2x+3=9 2x+3=9

Subtract 3 from both sides:

2x=6 2x=6

Divide both sides by 2:

x=3 x=3

For the second equation:

2x+3=−9 2x+3=-9

Subtract 3 from both sides:

2x=−12 2x=-12

Divide both sides by 2:

x=−6 x=-6

Thus, the solutions are x=3 x=3 and x=−6 x=-6 .

3

Final Answer

x=3 x=3 , x=−6 x=-6

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

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