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Chapter 1: Q. 30PT (page 51)

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

3y-1>5

Short Answer

Expert verified

Solution set of inequality is y|y<-43ory>2.

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. Description of step.

For all real numbers p] and q, q>0,

Case1) If p<qthen -q<p<q.

Case2) If p>qthen p>qorp<-q.

03

Step 3. Description of step.

Apply case 1 to 3y-1>5 which implies 3y-1>5 or 3y-1<-5.

04

Step 4. Description of step.

To solve given inequality, use subtraction and division properties of inequality. Add 1 on each side then divide each side by 3 and simplify.

3y鈭�1+1>5+13y3>63y>2
05

Step 5. Description of step.

Add 1 on each side then divide each side by 3 and simplify.

3y鈭�1+1<鈭�5+13y3<鈭�43y<鈭�43

Thus, solution is y>2 or y<-43.

06

Step 6. Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than -43 or greater than 2.

Write the solution set builder notation.

y|y<-43ory>2
07

Step 7. Graph the solution set.

Open circle on 2 and -43 shows these points are excluded in the solution set.

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Most popular questions from this chapter

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MEDICINE

Suppose a patient must take a blood pressure medication that is dispensed in 125-milligram tablets. The dosage is 15 milligrams per kilo gram of body weight and is given every 8 hours. If the patient weighs 25 kilograms, how many tablets would be needed for a 30-day supply? Use the formula n=24d梅8b脳15梅125, wheren is the number of tablets,d is the number of days the supply should last, andb is the body weight of the patient in kilograms.

Find the value of each expression

10-8梅2
See all solutions

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