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Chapter 1: Q. 27 (page 51)

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

53x-5+x<24x-1+1

Short Answer

Expert verified

Solution set of inequality is -鈭�,3.

Solution set on number line is

Step by step solution

01

Step 1. Write properties of inequality.

Properties of inequalities are written in following table:

02

Step 2. Solve 53x-5+x<24x-1+1.

To solve given inequality, use subtraction and division properties of inequality. Expand the parentheses on each side. Subtract 25 and then 8x from each side then divide each side by 8 and simplify.

15x鈭�25+x<8x鈭�2+116x鈭�25+25<8x鈭�1+2516x鈭�8x<8x+24鈭�8x8x8<248x<3

Thus, solution is x<3.

03

Step 3. Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than 3.

Write the solution set in interval notation.

-鈭�,3

04

Step 4. Graph the solution set.

Open circle on 3 shows this point is excluded in the solution set.

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