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Chapter 1: Q42. (page 50)

Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

42. n12+5鈮�7

Short Answer

Expert verified

Solution set of inequality is (-鈭�,24].

Solution set on number line is

Step by step solution

01

- Write properties of inequality.

Properties of inequalities are written in following table:

02

- Solve n12+5≤7.

To solve given inequality, use subtraction and multiplication properties of inequality. Subtract 5 from both the sides then multiply each side by 12 and simplify.

n12+5鈭�5鈮�7鈭�5n12鈰�12鈮�2鈰�12n鈮�24

Thus, solution is n鈮�24.

03

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than or equal to 24.

Write the solution set in interval notation.

(-鈭�,24]

04

– Graph the solution set.

Closed circle on 24 shows this point is included in the solution set.

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