Q23. - Algebra 1

Question

Solve each equation. Check your solution.

$\sqrt{5x}-1=4$

Step-by-Step Solution

Answer

The solution of the given equation is $x=5$.

 

Check:

Substitute 5 for x in the given equation $\sqrt{5x}-1=4$.

$$\begin{gathered} \sqrt{5x}-1=4 \\ \sqrt{5\left(5\right)}-1\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{25}-1\underset{¯}{\underset{¯}{?}}4 \\ 5-1\underset{¯}{\underset{¯}{?}}4 \\ 4=4 \end{gathered}$$

Therefore, $x=5$ is the solution of the given equation $\sqrt{5x}-1=4$.

Step 1. Rewrite the given equation.

The given equation can be written as:

$$\begin{gathered} \sqrt{5x}-1=4 \\ \sqrt{5x}=4+1 \\ \sqrt{5x}=5 \end{gathered}$$

Step 2. Solve the given equation.

The solution of the given equation is:

$$\begin{gathered} \sqrt{5x}=5 \\ {\left(\sqrt{5x}\right)}^2=5^2\left(\text{squaring both sides}\right) \\ 5x=25 \\ x=\frac{25}{5} \\ x=5 \end{gathered}$$

Therefore, the solution of the given equation is $x=5$.

Step 3. Check the solution.

Substitute 5 for x in the given equation $\sqrt{5x}-1=4$.

$$\begin{gathered} \sqrt{5x}-1=4 \\ \sqrt{5\left(5\right)}-1\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{25}-1\underset{¯}{\underset{¯}{?}}4 \\ 5-1\underset{¯}{\underset{¯}{?}}4 \\ 4=4 \end{gathered}$$

Therefore, $x=5$ is the solution of the given equation $\sqrt{5x}-1=4$.