Chapter 1: Q23. (page 51)

Solve each equation. Check your solution.
23. $12 |\frac{1}{2} y + 3| = 6$

Short Answer

Expert verified

The solution set of given equation is $\{- 5, - 7\}$ .

Step by step solution

– Description of step.

Divide each side of the given equation by 12 and simplify.

$\begin{matrix} \frac{12 |\frac{1}{2} y + 3|}{12} = \frac{6}{12} \\ |\frac{1}{2} y + 3| = \frac{1}{2} \end{matrix}$

– 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 $|\frac{1}{2} y + 3| = \frac{1}{2}$ and simplify.

$\begin{matrix} \frac{1}{2} y + 3 = \frac{1}{2} \\ \frac{1}{2} y + 3 - 3 = \frac{1}{2} - 3 \\ \frac{1}{2} y = - \frac{5}{2} \\ y = - 5 \end{matrix}$

– Description of step.

Apply case 2 mentioned in step 2 to $|\frac{1}{2} y + 3| = \frac{1}{2}$ and simplify.

$\begin{matrix} \frac{1}{2} y + 3 = - \frac{1}{2} \\ \frac{1}{2} y + 3 - 3 = - \frac{1}{2} - 3 \\ \frac{1}{2} y = - \frac{7}{2} \\ y = - 7 \end{matrix}$

– Description of step.

To check whether the obtained value of x is the solution of given equation, substitute $- 5$ for $y$ into $12 |\frac{1}{2} y + 3| = 6$ and simplify.

$\begin{array}{c} 12 |\frac{1}{2} (- 5) + 3| = 6 \\ 12 |\frac{1}{2}| \overset{?}{=} 6 \\ 12 \cdot \frac{1}{2} \overset{?}{=} 6 \\ 6 \overset{?}{=} 6 \\ 6 = 6 \end{array}$

– Description of step.

To check whether the obtained value of x is the solution of given equation, substitute $- 7$ for y into $12 |\frac{1}{2} y + 3| = 6$ and simplify.

$\begin{array}{c} 12 |\frac{1}{2} (- 7) + 3| = 6 \\ 12 |- \frac{1}{2}| \overset{?}{=} 6 \\ 12 \cdot \frac{1}{2} \overset{?}{=} 6 \\ 6 \overset{?}{=} 6 \\ 6 = 6 \end{array}$

Therefore, the solution set of given equation is $\{- 5, - 7\}$ .

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Solve each equation. Check your solution.
23. $12 |\frac{1}{2} y + 3| = 6$

Short Answer

Step by step solution

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

– Description of step.

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Solve each equation. Check your solution.23. 1212y+3=6

Short Answer

Step by step solution

– Description of step.

– 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

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution.
23. $12 |\frac{1}{2} y + 3| = 6$