Question

In the following exercises solve:

$3\sqrt{2x-3}-20=7$.

Short answer

The solution is,$x=42$.

Step-by-step solution

Step 1. Given Information.

The expression is,

$3\sqrt{2x-3}-20=7$.

Step 2. Finding the solution.

$3\sqrt{2x-3}-20=7$

Adding $20$both sides,

$$\begin{gathered} \Rightarrow 3\sqrt{2x-3}=7+20 \\ \Rightarrow 3\sqrt{2x-3}=27 \end{gathered}$$

Dividing $3$both sides,

$$\begin{gathered} \Rightarrow \frac{3\sqrt{2x-3}}{3}=\frac{27}{3} \\ \Rightarrow \sqrt{2x-3}=9 \end{gathered}$$

Squaring both sides,

$$\begin{gathered} \Rightarrow {\left(\sqrt{2x-3}\right)}^2=9^2 \\ \Rightarrow 2x-3=81 \end{gathered}$$

Adding $3$both sides,

$$\begin{gathered} \Rightarrow 2x=81+3 \\ \Rightarrow 2x=84 \end{gathered}$$

Dividing $2$both sides,

$$\begin{gathered} \Rightarrow \frac{2x}{2}=\frac{84}{2} \\ \Rightarrow x=42 \end{gathered}$$

Step 3. Checking the solution.

$3\sqrt{2x-3}-20$

Inputting $x=42$,

$$\begin{gathered} =3\sqrt{2\times 42-3}-20 \\ =3\sqrt{84-3}-20 \\ =3\sqrt{81}-20 \\ =3\times 9-20 \\ =27-20 \\ =7 \end{gathered}$$

The solution is true.