Q40. - Algebra 1

Question

Solve each equation. Check your solution.

$\sqrt{3x}=2$

Step-by-Step Solution

Answer

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

 

Check:

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

width="83" height="123" style="max-width: none; vertical-align: -62px;" $$\begin{gathered} \sqrt{3x}=2 \\ \sqrt{3\left(\frac{4}{3}\right)}=2 \\ \sqrt{4}=2 \\ \therefore 2=2 \end{gathered}$$ 

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

Step 1. Rewrite the given equation.

The given equation can be written as:

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

Step 2. Solve the given equation.

The solution of the given equation is:

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

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

Step 3. Check the solution.

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

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

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