Q66. Solve each equation. Check your ... [FREE SOLUTION]

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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 $q 鈮� 0$ ,

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.

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

– Description of step.

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

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

– 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.

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

Therefore, the solution set of given equation is

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91影视

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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91影视

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

Logic and Functions

Discrete Mathematics

Geometry

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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