Question

solve each absolue value equation

7. |3x-1|=|x+4|

Answer 1

Solve

$$|3x - 1| = |x + 4|$$ $$\left[ \begin{array}{l} 3x - 1 = x + 4 \\ 3x - 1 = -x - 4 \end{array} \right. \Rightarrow \left[ \begin{array}{l} x = \frac{5}{2} \\ x = -\frac{3}{4} \end{array} \right. \quad \Rightarrow \quad \left[ \begin{array}{l} x = 2\frac{1}{2} \\ x = -\frac{3}{4} \end{array} \right.$$

Answer: $-\frac{3}{4}$; $2\frac{1}{2}$