Chapter 2.5, Problem 42PPS

To determine

To Solve and graph: The equation $\frac{4}{\left|p\right|}+12=14$

Answer to Problem 42PPS

The required solution is $p=2$

$p=-2$

Explanation of Solution

Given information:

The equation $\frac{4}{\left|p\right|}+12=14$

Calculation:

  $\frac{4}{\left|p\right|}+12=14$

  $\Rightarrow \frac{4}{\left|p\right|}+12-12=14-12$

(Subtract 12 from both sides)

  $\Rightarrow \frac{4}{\left|p\right|}=2$   (Simplify)

  $\Rightarrow \frac{4\left|p\right|}{\left|p\right|}=2\left|p\right|$

(Multiply by $\left|p\right|$ on both sides)

  $\Rightarrow 4=2\left|p\right|$   (Simplify)

So, we can rewrite the equation as: $2\left|p\right|=4$

Case 1

  $\Rightarrow 2p=4$

  $\Rightarrow \frac{2p}{2}=\frac{4}{2}$

(Divide by 2 on both sides)

  $\Rightarrow p=2$   (Simplify)

Case2

  $\Rightarrow 2p=-4$

  $\Rightarrow \frac{2p}{2}=\frac{-4}{2}$

(Divide by 2 on both sides)

  $\Rightarrow p=-2$

((Simplify)

Therefore, the required solution is $p=2$

$p=-2$