Question

In the following exercises, solve:

$3\sqrt{7y+1}-10=8$.

Short answer

The solution is,$y=5$.

Step-by-step solution

Step 1. Given Information.

The expression is,

$3\sqrt{7y+1}-10=8$.

Step 2. Finding the solution.

$3\sqrt{7y+1}-10=8$

Adding $10$on both sides,

$$\begin{gathered} \Rightarrow 3\sqrt{7y+1}=8+10 \\ \Rightarrow 3\sqrt{7y+1}=18 \end{gathered}$$

Dividing $3$by both sides,

$$\begin{gathered} \Rightarrow \frac{3\sqrt{7y+1}}{3}=\frac{18}{3} \\ \Rightarrow \sqrt{7y+1}=6 \end{gathered}$$

Squaring both sides,

$$\begin{gathered} \Rightarrow {\left(\sqrt{7y+1}\right)}^2=6^2 \\ \Rightarrow 7y+1=36 \end{gathered}$$

Subtracting $1$on both sides,

$$\begin{gathered} \Rightarrow 7y=36-1 \\ \Rightarrow 7y=35 \end{gathered}$$

Dividing $7$by both sides,

$$\begin{gathered} \Rightarrow \frac{7y}{7}=\frac{35}{7} \\ \Rightarrow y=5 \end{gathered}$$

Step 3. Checking the solutions.

$3\sqrt{7y+1}-10$

Inputting $y=5$,

$$\begin{gathered} =3\sqrt{7\times 5+1}-10 \\ =3\sqrt{35+1}-10 \\ =3\sqrt{36}-10 \\ =3\times 6-10 \\ =18-10 \\ =8 \end{gathered}$$

The solution is true.