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Chapter 5: Q8. (page 302)

Define a variable, write an inequality, and solve each problem. Check your solution.

Twice a number increased by 3 is less than the number decreased by 4.

Short Answer

Expert verified

The variable is x is and the inequality equation is 2x+3<x鈭�4. The solution for the inequality is x<鈭�7.

Step by step solution

01

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol 鈮�or鈮�, use the bracket or a solid circle at that endpoint.

Properties of inequality:

1.b鈮�c鈬�b卤a鈮�c卤a2.b鈮�c鈬�ab鈮�ac,ifa>03.b鈮�c鈬�ab鈮�ac,ifa<0

02

Step 2. Write the inequality for the given condition.

Let the number be x.

Twice a number increased by 3 is less than the number decreased by 4:

2x+3<x鈭�4

03

Step 3. Solve for x.

Solve for x in the inequation 2x+3<x鈭�4.

2x+3<x鈭�42x+3鈭�3<x鈭�4鈭�32x<x鈭�72x鈭�x<x鈭�7鈭�xx<鈭�7

04

Step 4. Check the solution when x=-10.

Put the value of xas 鈭�10.

2x+3<x鈭�42鈭�10+3<鈭�10鈭�4鈭�20+3<鈭�14鈭�17<鈭�14TrueStatement

Thus, the solution of the inequality equation 2x+3<x鈭�4is x<鈭�7.

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Most popular questions from this chapter

Solve each inequality. Check your solution.

2x+11鈮�5x鈭�10

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鈭�9m<鈭�36

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F role="math" localid="1647844731947" {p|p鈮�10}

G{p|p鈮�10}

H{p|p鈮�26}

J{p|p鈮�126}

Solve each inequality. Then graph it on a number line.

w鈭�4>9

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