Solve for x |x+4|=|2x+1|

Problem

|x+4|=|2*x+1|

Solution

1. Apply the property of absolute value equalities, which states that if |a|=|b| then a=b or a=−b

2. Set up the first case where the expressions inside the absolute value bars are equal to each other.

x+4=2*x+1

3. Solve for x in the first case by subtracting x and 1 from both sides.

4−1=2*x−x

3=x

4. Set up the second case where one expression is equal to the negative of the other.

x+4=−(2*x+1)

5. Distribute the negative sign on the right side of the equation.

x+4=−2*x−1

6. Solve for x in the second case by adding 2*x to both sides and subtracting 4 from both sides.

3*x=−5

x=−5/3

Final Answer

x=3,−5/3

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