Question

Find the real solutions of the equation $\left|2x\right|=3$.

Short answer

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

Step-by-step solution

Step 1. Remove the modulus sign of given equation.

$$\begin{gathered} \left|2x\right|=3....\left(\text{Given}\right) \\ \text{or}2x=\pm 3 \\ 2x=3\text{or}2x=-3....\left(1\right) \end{gathered}$$

Step 2. Further simplify (1).

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

Step 3. DESCRIPTION OF STEPS.

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