Chapter 9: Q. 413 (page 1108)

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

Short Answer

Expert verified

The solution is, $x = 3$ .

Step by step solution

Step 1. Given Information.

The expression is,

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

Step 2. Finding the solution.

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

Adding $8$ on both sides,

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

Dividing $2$ on both sides,

$\Rightarrow \frac{2 \sqrt{5 x + 1}}{2} = \frac{8}{2} \Rightarrow \sqrt{5 x + 1} = 4$

Squaring both sides,

role="math" localid="1647889338838" $\Rightarrow {(\sqrt{5 x + 1})}^{2} = {(4)}^{2} \Rightarrow 5 x + 1 = 16$

Subtracting $1$ both sides,

$\Rightarrow 5 x = 16 - 1 \Rightarrow 5 x = 15$

Dividing $5$ both sides,

$\Rightarrow \frac{5 x}{5} = \frac{15}{5} \Rightarrow x = 3$

Step 3. Checking the solution.

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

Inputting $x = 3$ ,

$= 2 \sqrt{5 \times 3 + 1} - 8 = 2 \sqrt{15 + 1} - 8 = 2 \sqrt{16} - 8 = 2 \times 4 - 8 = 8 - 8 = 0$

The solution is true.

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the solution.

Step 3. Checking the solution.

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Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the solution.

Step 3. Checking the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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