Chapter 1: Q66. (page 46)

Solve each equation. Check your solutions.
66. $|2 x + 7| = 15$

Short Answer

Expert verified

The solution set of given equation is $\{4, - 11\}$ .

Step by step solution

– Description of step.

For any real numbers $p$ and $q$ , where $q \geq 0$ ,

Case 1) if $|p| = q$ then $p = q$ or

Case 2) if $|p| = q$ then $p = - q$

– Description of step.

Apply case 1 mentioned in step 2 to $|2 x + 7| = 15$ and simplify.

$\begin{array}{l} 2 x + 7 = 15 \\ 2 x + 7 - 7 = 15 - 7 \\ \frac{2 x}{2} = \frac{8}{2} \\ x = 4 \end{array}$

– Description of step.

Apply case 2 mentioned in step 2 to $|2 x + 7| = 15$ and simplify.

$\begin{array}{l} 2 x + 7 = - 15 \\ 2 x + 7 - 7 = - 15 - 7 \\ \frac{2 x}{2} = \frac{- 22}{2} \\ x = - 11 \end{array}$

– Description of step.

To check whether the obtained value of $x$ is the solution of given equation, substitute 4 for $x$ into $|2 x + 7| = 15$ and simplify.

$\begin{array}{l} |2 x + 7| = 15 \\ |2 (4) + 7| \overset{?}{=} 15 \\ |8 + 7| \overset{?}{=} 15 \\ |15| \overset{?}{=} 15 \\ 15 = 15 \end{array}$

– Description of step.

To check whether the obtained value of $x$ is the solution of given equation, substitute $- 11$ for $x$ into $|2 x + 7| = 15$ and simplify.

$\begin{array}{c} |2 x + 7| = 15 \\ |2 (- 11) + 7| \overset{?}{=} 15 \\ |- 22 + 7| \overset{?}{=} 15 \\ |- 15| \overset{?}{=} 15 \\ 15 = 15 \end{array}$

Therefore, the solution set of given equation is

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Solve each equation. Check your solutions.
66. $|2 x + 7| = 15$

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

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Solve each equation. Check your solutions.66. 2x+7=15

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solutions.
66. $|2 x + 7| = 15$