In the following exercises, solve.25x+1-8=0

Q. 320 - Intermediate Algebra

In the following exercises, solve.
$2 \sqrt{5 x + 1} - 8 = 0$

Verified

Answer

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

1Step 1. Given information.

The given equation is:

$2 \sqrt{5 x + 1} - 8 = 0$

2Step 2. Simplify the equation.

The given equation can be written as:

$2 \sqrt{5 x + 1} = 8$

Divide both sides by 2.

$\begin{array}{rcl} \sqrt{5 x + 1} & = & \frac{8}{2} \\ \sqrt{5 x + 1} & = & 4 \end{array}$

3Step 3. Solve the equation.

Take square on both sides.

$\begin{array}{rcl} (\sqrt{5 x + 1})^{2} & = & (4)^{2} \\ 5 x + 1 & = & 16 \\ 5 x & = & 16 - 1 \\ 5 x & = & 15 \end{array}$

Divide both sides by 5.

$\begin{array}{rcl} \frac{5 x}{5} & = & \frac{15}{5} \\ x & = & 3 \end{array}$

4Step 4. Conclusion.

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