Question

Solve each equation. Check your solution.

$\sqrt{x+1}+2=4$

Short answer

The solution of the given equation is $x=3$.

Check:

Substitute 3 for x in the given equation $\sqrt{x+1}+2=4$.

$$\begin{gathered} \sqrt{x+1}+2=4 \\ \sqrt{3+1}+2\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{4}+2\underset{¯}{\underset{¯}{?}}4 \\ \text{2+2}\underset{¯}{\underset{¯}{?}}4 \\ \text{4}=4 \end{gathered}$$

Therefore,$x=3$is the solution of the given equation $\sqrt{x+1}+2=4$.

Step-by-step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$$\begin{gathered} \sqrt{x+1}+2=4 \\ \sqrt{x+1}=4-2 \\ \sqrt{x+1}=2 \\ {\left(\sqrt{x+1}\right)}^2=2^2\left(\text{squaringbothsides}\right) \\ x+1=4 \end{gathered}$$

Step 2. Solve the given equation.

The solution of the given equation is:

$$\begin{gathered} x+1=4 \\ x=4-1 \\ x=3 \end{gathered}$$

Therefore, the solution of the given equation is $x=3$.

Step 3. Check the solution.

Substitute 3 for x in the given equation $\sqrt{x+1}+2=4$.

$$\begin{gathered} \sqrt{x+1}+2=4 \\ \sqrt{3+1}+2\underset{¯}{\underset{¯}{?}}4 \\ \sqrt{4}+2\underset{¯}{\underset{¯}{?}}4 \\ \text{2+2}\underset{¯}{\underset{¯}{?}}4 \\ \text{4}=4 \end{gathered}$$

Therefore,$x=3$ is the solution of the given equation $\sqrt{x+1}+2=4$.