Q25. - Algebra 1

Question

Solve each equation. Check your solution.

$\sqrt{15-x}=4$

Step-by-Step Solution

Answer

The solution of the given equation is $x=-1$.

 

Check:

Substitute $-1$ for x in the given equation $\sqrt{15-x}=4$.

$$\begin{gathered} \sqrt{15-x}=4 \\ \sqrt{15-\left(-1\right)}\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{15+1}\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{16}\underset{¯}{\underset{¯}{?}}4 \\ \text{ 4}=4 \end{gathered}$$

Therefore, $x=-1$ is the solution of the given equation $\sqrt{15-x}=4$.

Step 1. Rewrite the given equation.

The given equation can be written as:

$$\begin{gathered} \sqrt{15-x}=4 \\ {\left(\sqrt{15-x}\right)}^2=4^2\left(\text{squaring both sides}\right) \\ 15-x=16 \end{gathered}$$

Step 2. Solve the given equation.

The solution of the given equation is:

$$\begin{gathered} 15-x=16 \\ 15-16=x \\ -1=x \end{gathered}$$

Therefore, the solution of the given equation is $x=-1$.

Step 3. Check the solution.

Substitute $-1$ for x in the given equation $\sqrt{15-x}=4$.

$$\begin{gathered} \sqrt{15-x}=4 \\ \sqrt{15-\left(-1\right)}\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{15+1}\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{16}\underset{¯}{\underset{¯}{?}}4 \\ \text{ 4}=4 \end{gathered}$$

Therefore, $x=-1$ is the solution of the given equation $\sqrt{15-x}=4$.