**Double Inequalities Practice Problems**

**Set 1: Double Inequalities **

To review double inequalities, go to Double Inequalities Help

**Practice**

Give the interval notation and shade the region on the number line for the double inequality.

**Solutions**

**Set 2: The Three Sides of Double Inequalities **

To review interval notation, go to Double Inequalities Help.

**Practice**

Give your solution in interval notation.

**Solutions**

**Set 3: Double Inequalities with Two Variables **

Double Inequalities are used to solve word problems where the solution is a limited range of values. Usually there are two variables and you are givien the range of one of them and asked to find the range of the other. To review this concept, go to Double Inequalities Help.

**Practice**

Give the corresponding interval for x.

**Solutions**

**Set 4: Double Inequality Word Problems **

To review double inequalities in applied problems, go to Double Inequalities Help.

**Practice**

- According to Hooke’s Law, the force,
*F*(in pounds), required to stretch a certain spring*x*inches beyond its natural length is*F*= 4.2*x*. If 7 ≤*F*≤ 14, what is the corresponding range for*x*? - Recall that the relationship between the Fahrenheit and Celsius temperature scales is given by . If 5 ≤ F ≤ 23, what is the corresponding range for C?
- A saleswoman’s salary is a combination of an annual base salary of $15,000 plus a 10% commission on sales. What level of sales does she need to maintain in order that her annual salary range from $25,000 to $40,000?
- The Smith’s electric bills consist of a base charge of $20 plus 6 cents per kilowatt-hour. If the Smiths want to keep their electric bill in the $80 to $110 range, what range of kilowatt-hours do they need to maintain?
- A particular collect call costs $2.10 plus 75 cents per minute. (The company bills in two-second intervals.) How many minutes would a call need to last to keep a charge between $4.50 and $6.00?

**Solutions**

- 7 ≤
*F*≤ 14 and*F*= 4.2*x*.If the force is to be kept between 7 and 14 pounds, the spring will stretch between and inches beyond its natural length.

- 5 ≤ F ≤ 23 and and .
- Let
*x*represent the saleswoman’s annual sales. Let*s*= 15,000 + 0.10*x*represent her annual salary. She wants 25,000 ≤ s ≤ 40,000.She needs to have her annual sales range from $100,000 to $250,000 in order to maintain her annual salary between $25,000 and $40,000.

- Let
*x*represent the number of kilowatt-hours the Smiths use per month. Then*c*= 20 + 0.06*x*represents their monthly electric bill.The Smiths would need to keep their monthly usage between 1000 and 1500 kilowatt-hours monthly to keep their monthly bills in the $80 to $110 range.

- Let
*x*represent the number of minutes the call lasts. Let*c*= 2.10 + 0.75*x*represent the total cost of the call.3.2 minutes is three minutes 12 seconds and 5.2 minutes is five minutes 12 seconds because 0.20 minutes is 0.20(60) seconds = 12 seconds

A call would need to last between three minutes 12 seconds and 5 minutes 12 seconds in order to cost between $4.50 and $6.00.

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