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Chapter 1: Q63. (page 46)

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

63. 3n+4n+3<5n+2

Short Answer

Expert verified

Solution set of inequality is (-鈭�,-1).

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 3n+4n+3<5n+2.

To solve given inequality, use subtraction and division properties of inequality. To solve given inequality, expand the parentheses on each side. Subtract 12 from each side then subtract 5nfrom each side and then divide each side of the inequality by 2

3n+4n+12<5n+107n+12鈭�12<5n+10鈭�127n鈭�5n<5n鈭�2鈭�5n2n2<鈭�22n<鈭�1

Thus, solution is n<-1.

03

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than -1.

Write the solution set in interval notation.

(-鈭�,-1)

04

– Graph the solution set

Open circle on 鈭�1shows this point is excluded in the solution set

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