Question

Solve the equation$5\left|3x-4\right|=x+1$.

Short answer

The given equation has the solution$x=\frac{3}{2}\text{or}x=\frac{19}{16}$

Step-by-step solution

Step 1. Write down the given equation.

The given equation is$5\left|3x-4\right|=x+1$.

Step 2. Simplify the equation.

The given equation $5\left|3x-4\right|=x+1$is solved as:

$\begin{array}{c}5\left|3x-4\right|=x+\mathrm{1....}\left(\text{Given}\right)\\ \left|3x-4\right|=\frac{x+1}{5}\\ 3x-4=\pm \frac{x+1}{5}\\ 3x-4=\frac{x+1}{5}\text{or}3x-4=-\frac{x+1}{5}\\ 15x-20=x+1\text{or}15x-20=-x-1\\ x=\frac{3}{2}\text{or}x=\frac{19}{16}\end{array}$

Step 3. Conclusion.

The given equation has the solution$x=\frac{3}{2}\text{or}x=\frac{19}{16}$.