Chapter 2: Q54. (page 142)

Solve each equation. Then graph the solution set.
$|\frac{2 b}{3} + 8| = 20$

Short Answer

Expert verified

The Solution set is ${- 42, 18}$ .

Step by step solution

Step 1. Case when the modulus expression is positive.

The absolute value or modulus of a real number x, denoted $|x|$ , it is the non-negative value of $x$ without regard to its sign.

$|x| = x$ if $x$ is positive,

$|x| = - x$ if $x$ is negative,

$|0| = 0$ .

For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.

We are given the expression $|\frac{2 b}{3} + 8| = 20$ assuming a positive value for the modulus expression we get:

role="math" localid="1643047735974" $\begin{array}{l} \frac{2 b}{3} + 8 = 20 \\ \frac{2 b}{3} = 20 - 8 \\ \frac{2 b}{3} = 12 \\ 2 b = 12 (3) \\ b = \frac{36}{2} \\ b = 18 \end{array}$

Thus $b = 18$ is one of the solutions.

Step 2. Case when the modulus expression is negative.

$\begin{array}{l} \frac{2 b}{3} + 8 = - 20 \\ \frac{2 b}{3} = - 20 - 8 \\ \frac{2 b}{3} = - 28 \\ 2 b = - 28 (3) \\ b = \frac{- 84}{2} \\ b = - 42 \end{array}$

Thus $b = - 42$ is one of the solutions.

Step 3. Graphing the solution set.

The solution set is ${- 42, 18}$ , we graph these values on the number line as shown below:

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Solve each equation. Then graph the solution set.
$|\frac{2 b}{3} + 8| = 20$

Short Answer

Step by step solution

Step 1. Case when the modulus expression is positive.

Step 2. Case when the modulus expression is negative.

Step 3. Graphing the solution set.

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Solve each equation. Then graph the solution set.2b3+8=20

Short Answer

Step by step solution

Step 1. Case when the modulus expression is positive.

Step 2. Case when the modulus expression is negative.

Step 3. Graphing the solution set.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Mechanics Maths

Geometry

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each equation. Then graph the solution set.
$|\frac{2 b}{3} + 8| = 20$