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Chapter 2: Q54. (page 142)

Solve each equation. Then graph the solution set.

2b3+8=20

Short Answer

Expert verified

The Solution set is {鈭�42,18}.

Step by step solution

01

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 xwithout regard to its sign.

x=xif xis positive,

x=鈭�xif xis negative,

0=0.

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

We are given the expression 2b3+8=20assuming a positive value for the modulus expression we get:

role="math" localid="1643047735974" 2b3+8=202b3=20鈭�82b3=122b=123b=362b=18

Thus b=18is one of the solutions.

02

Step 2. Case when the modulus expression is negative.

2b3+8=鈭�202b3=鈭�20鈭�82b3=鈭�282b=鈭�283b=鈭�842b=鈭�42

Thus b=鈭�42is one of the solutions.

03

Step 3. Graphing the solution set.

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

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