Q40. - Algebra 1

Question

Solve each equation. Check your solution.

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

Step-by-Step Solution

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

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

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 1. Rewrite the given equation.

The given equation can be written as:

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

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 $\sqrt{3x}=2$.