Question

Find the real solutions of the equation $\left|3x+5\right|=1$.

Short answer

The given equation has two real solutions $x=-2,-\frac{4}{3}$.

Step-by-step solution

Step 1. Remove the modulus sign of given equation.

$$\begin{gathered} \left|3x+5\right|=1....\left(\text{Given}\right) \\ \text{or}3x+5=\pm 1 \\ 3x+5=1\text{or}3x+5=-1....\left(1\right) \end{gathered}$$

Step 2. Further simplify (1).

$$\begin{gathered} 3x+5=1\text{or}3x+5=-1....\left(\text{From}\left(1\right)\right) \\ 3x=1-5\text{or}3x=-1-5 \\ 3x=-4\text{or}3x=-6 \\ x=-\frac{4}{3}\text{or}x=-2 \end{gathered}$$

Step 3. Description of steps.

From the obtained values of solution the real solutions of the equation are$x=-2,-\frac{4}{3}$ and both of these solutions satisfy the given equation.