Question

Solve each equation. Check your solution.

$\sqrt{\mathbf{3}\mathbf{x}}\mathbf{=}\mathbf{2}$

Short answer

The solution of the given equation is $\mathit{x}\mathbf{=}\frac{\mathbf{4}}{\mathbf{3}}$.

Check:

Substitute $\frac{\mathbf{4}}{\mathbf{3}}$for $\mathit{x}$in the given equation $\sqrt{\mathbf{3}\mathbf{x}}\mathbf{=}\mathbf{2}$.

role="math" localid="1648098319617" $\begin{array}{l}\sqrt{\mathbf{3}\mathbf{x}}\mathbf{=}\mathbf{2}\\ \sqrt{\mathbf{3}\left(\frac{\mathbf{4}}{\mathbf{3}}\right)}\mathbf{=}\mathbf{2}\\ \sqrt{\mathbf{4}}\mathbf{=}\mathbf{2}\\ \mathbf{\therefore }\mathbf{2}\mathbf{=}\mathbf{2}\end{array}$

Therefore, $\mathit{x}\mathbf{=}\frac{\mathbf{4}}{\mathbf{3}}$is the solution of the given equation $\sqrt{\mathbf{3}\mathbf{x}}\mathbf{=}\mathbf{2}$.

Step-by-step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$\begin{array}{l}\sqrt{3x}=2\\ {\left(\sqrt{3x}\right)}^2=2^2\left(\text{squaringbothsides}\right)\\ 3x=4\end{array}$

Step 2. Solve the given equation.

The solution of the given equation is:

$\begin{array}{l}3x=4\\ \frac{3x}{3}=\frac{4}{3}\\ x=\frac{4}{3}\end{array}$

Therefore, the$x$ value of is $\frac{4}{3}$.

Step 3. Check the solution.

Substitute$\frac{4}{3}$ for$x$ in the given equation $\sqrt{3x}=2$.

$\begin{array}{l}\sqrt{3x}=2\\ \sqrt{3\left(\frac{4}{3}\right)}\underset{¯}{\underset{¯}{?}}2\\ \sqrt{4}\underset{¯}{\underset{¯}{?}}2\\ \text{2}=2\end{array}$

Therefore,$x=\frac{4}{3}$ is the solution of the given equation $\sqrt{3x}=2$.