Chapter 2: Q42. (page 106)

Solve each equation. Then graph the solution set.
$\frac{4}{|p|} + 12 = 14$

Short Answer

Expert verified

The equation $\frac{4}{|p|} + 12 = 14$ has solution set as $p = 2, - 2$ and the graph of the solution set is:

Step by step solution

Step-1. Define absolute value equation.

For any real numbers a and b, if $|a| = b$ and $b \geq 0$ , then $a = b$ or $a = - b$ .

Step-2. Formulate case 1 when p=p.

Simplify the expression for p.

$\begin{matrix} \frac{4}{p} + 12 - 12 = 14 - 12 \\ \frac{4}{p} \times p = 2 \times p \\ 4 = 2 p \\ \frac{4}{2} = \frac{2 p}{2} \\ p = 2 \end{matrix}$

Step-3. Formulate case 2 when p=−p.

Simplify the expression for p.

$\begin{matrix} \frac{4}{(- p)} + 12 - 12 = 14 - 12 \\ \frac{4}{(- p)} \times (p) = 2 \times p \\ - 4 = 2 p \\ \frac{- 4}{2} = \frac{2 p}{2} \\ p = - 2 \end{matrix}$

Step-4. Plot the graph of the solution set.

From case 1 and case 2, $p = 2, - 2$ . Plot these values on the number line.

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Solve each equation. Then graph the solution set.
$\frac{4}{|p|} + 12 = 14$

Short Answer

Step by step solution

Step-1. Define absolute value equation.

Step-2. Formulate case 1 when p=p.

Step-3. Formulate case 2 when p=−p.

Step-4. Plot the graph of the solution set.

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Solve each equation. Then graph the solution set.4p+12=14

Short Answer

Step by step solution

Step-1. Define absolute value equation.

Step-2. Formulate case 1 when p=p.

Step-3. Formulate case 2 when p=−p.

Step-4. Plot the graph of the solution set.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Logic and Functions

Calculus

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation. Then graph the solution set.
$\frac{4}{|p|} + 12 = 14$