Q. 8.111 - Intermediate Algebra

Question

Solve: $\sqrt{3m + 2} - 5 = 0.$

Step-by-Step Solution

Answer

The solution is $m=\frac{23}{3}$.

Step 1 Given equation is,

$\sqrt{3m + 2} - 5 = 0.$

To isolate the radical add $5$ on both sides.

$$\begin{gathered} \sqrt{3m + 2} - 5 +5=5 \\ \sqrt{3m + 2} =5 \end{gathered}$$

Now square on both the sides.

$$\begin{gathered} 3m+2={\left(5\right)}^2 \\ 3m+2=25 \end{gathered}$$

Step 2 Now simplify the obtained equation.

$$\begin{gathered} 3m+2=25 \\ 3m=25-2 \\ 3m=23 \\ m=\frac{23}{3} \end{gathered}$$

Step 3 Let us check the answer.

$$\begin{gathered} \sqrt{3\left(\frac{23}{3}\right) + 2} - 5 = 0 \\ \sqrt{23+2}-5=0 \\ \sqrt{25}-5=0 \\ 5-5=0 \\ 0=0 \end{gathered}$$

which is true.