Solve for x |x+3|=|2x+1|

Problem

|x+3|=|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:

x+3=2*x+1

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

3−1=2*x−x

x=2

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

x+3=−(2*x+1)

5. Distribute the negative sign on the right side:

x+3=−2*x−1

6. Solve for x in the second case by adding 2*x and subtracting 3 from both sides:

3*x=−4

x=−4/3

Final Answer

x=2,−4/3

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