Elementary and Intermediate Algebra: Inequality and Slope-Intercept

Simplify (4x + 2)3. 2. Janice is buying paint to paint her new apartment. The store sells paint in one-gallon cans. How accurate does her estimate need to be for the amount of paint needed? 3. A city planner is measuring the distance of one city block. Which unit of measure should she use: 1 mile, 1 meter, inch? 4. A book club earns $230 for its meetings. They want to divide the money to pay for 7 meetings. When the treasurer types 230 ÷ 7 into a calculator, the number that appears is 32.8571. Where should the treasurer round the answer? Explain. 5. Kalen is trying to find the average of three measurements. The measurements are 13.8, 15.64, and 22.51. He adds the numbers and divides by three. The result on the calculator shows 17.3167. Where should Kalen round? Explain. 6. The Grand Theater has 13,451 seats. If 15,340 people need to be seated in the theater for a music concert, write and solve an equation to find the number of seats that need to be added to the theater to accommodate all the people. 7. The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F. Write and solve an equation to find the decrease in temperature. 8. A candle is 4 inches tall and burns at the rate of 0.6 inch per hour. If the height of the candle after x hours is 1.5 inches, write an equation to represent the situation. Then use this equation to find the expected number of hours in which the candle melted to 1.5 inches. 9. David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent. 10. A cliff on the seashore is eroding at the rate of 17 centimeters per year. Write and solve an equation to find the number of years in which the cliff will erode 85 centimeters. 11. The slope of a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be translated to the left or right to represent the same function d(x)? Explain your answer. 12. Building codes regulate the steepness of stairs. Homes must have steps that are at least 13 inches wide for each 8 inches that they rise. a. Discuss how to find the slope of the stairs. b. Describe how changing the width or height affects the steepness of the stairs. Write a function with a zero of . Explain how you know. 14. Catherine found that as she increases the price of a chocolate bar, the number of sales per week decreased. Week Number of Sales 1 149 2 143 3 137 4 131 5 125 a. Write a formula for the arithmetic sequence that represents the number of sales per week. b. Explain how you could use the information to predict the number of sales for the eighth week. 15. The temperature C, in degrees, that is equivalent to a temperature of F degrees Fahrenheit is given by . The graph of this equation shows the temperature in Celsius for the corresponding temperatures in Fahrenheit. a. Explain how linear equations can be used in temperature conversion. b. Explain how could you could use the conversion graph to find the normal body temperature in degrees Celsius, which is 98.6°F. 16. Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day. a. If both of them get $4.50 an hour, write an inequality to compare Peter’s and Cindy’s earnings. b. What should Cindy’s per-hour income be so that she earns at least $14 a day? Write an inequality and an explanation of how to solve it. 17. Admission prices to Cinema I to see a movie are $9.50 for an adult and $6.50 for a child. The admission charge at Cinema II is $8.00 per person regardless of age. a. Write an inequality showing that the prices are cheaper at Cinema I than at Cinema II. b. If 6 adults and their children go together to see a movie, use the inequality to find how many children must attend for Cinema I to be the better deal. 18. On a road in the city of Madison, the maximum speed is 45 miles per hour and the minimum speed is 35 miles per hour. Let x represents the speed. You can write two inequalities to represent the speed restrictions. The inequalities and can be combined and can be written without using and. a. Explain how compound inequalities can be use to describe the speed restrictions on roads. b. Include a compound inequality describing a possible age restriction for driving on roads. Describe what this represents. (Minimum driving age is 16 years, and most drivers stop renewing their licenses by age 100.) 19. A county government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm. a. Write and solve an absolute value inequality to represent this situation. b. A lifeguard measures the chlorine level in the pool and finds it is 1.0 ppm. Should he add more chlorine? Explain. 20. Carmen can buy bottles of paint for $2.00 each and boxes of colored pencils for $3.50 each. She can spend no more than $42 on art supplies. a. Write an inequality that shows how many bottles of paint, x, and boxes of colored pencils, y, Carmen can buy. b. Name three different solutions to the inequality.