Equation with two absolute values (|2x-1| = |x+3|)

Statement

Solve the equation $|2x-1|=|x+3|$.

Solution

Two equal absolute values mean equal or opposite arguments: $2x-1=x+3\ \lor\ 2x-1=-(x+3)$.

• $2x-1=x+3 \implies x=4$;
• $2x-1=-x-3 \implies 3x=-2 \implies x=-\frac23$.

Solution: $\boxed{x=4\ \lor\ x=-\dfrac23}$.

Links

Topics: Parabola
Concepts: Absolute value
Methods: Absolute value mixed cases
Skills: Solving equations
Exercise type: Solving an equation