2. 1.a) Translate the equation: Eight more than three times a number is 20. 3x + 8 = 20 3x = 12 − 8 x = 4 3 3 b) Solve the equation. 3x + 8 = 20 Subtract Divide © 2007-10 by S-Squared, Inc. All Rights Reserved.

3. 4x < 28 2.a) Translate the inequality: Four times the difference of a number and three is less than 16. 4(x – 3) < 16 + 12 x < 7 4 4 b) Solve the inequality. 4(x – 3) < 16 4x – 12 < 16 Add Divide Distribute

4. 3.The sum of 2 consecutive integers is 51. a)Write a variable equation for the given information. Assign variables: 2x = 50 − 1 x = 25 2 2 b) Find the integers. x + x + 1 = 51 The first integer is x Let, x = the 1 st integer and x + 1 = the 2 nd integer 2x + 1 = 51 1 st integer: 25 The second integer is x + 1 2 nd integer: 26 Subtract Divide Simplify

5. older than Gina. The sum of their ages is 29. 4.Carlie Jo is 8 years younger than Gina. Tuana is one year Assign variables: 3g = 36 + 7 g = 12 3 3 b) How old is each person? g + g – 8 + g + 1 = 29 Gina’s age is g Let, g = Gina’s age, g + 1 = Tuana’s age 3g – 7 = 29 Gina is 12 yrs old Carlie Jo is g – 8 g – 8 = Carlie Jo’s age, Carlie Jo is 4 yrs old Tuana is g + 1 Tuana is 13 yrs old Carlie Jo is 8 years younger than Gina Tuana is one year older than Gina The sum of their ages is 29 Add Divide Simplify a)Write a variable equation for the given information.

6. 15n = 195 5.Juanita has the same number of dimes as nickels. She has a total of $1.95. How much of each coin does she have?.10d +.05n = 1.95 n = 13 15 Write an equation..10n +.05n = 1.95 10n + 5n = 195 Combine Divide Multiply by 100 to eliminate decimal point Let, d = # of dimes, n = # of nickels, Since there is the same number of dimes as nickels, substitute n for d. She has 13 of each coin.

7. 5s = 270 6.Dwayne weighs two-thirds as much as his older sister. The sum of their weights is 90 lbs. How much does Dwayne weigh? d + s = 90 s = 54 5 5 Write an equation. s + s = 90 2s + 3s = 270 Combine Divide Multiply by 3 to eliminate fraction Let, d = Dwayne’s weight, s = Sister’s weight, Since Dwayne weighs two-thirds as much as his sister substitute. his sister substitute s for d. 2 3 2 3

8. sister = 54 pounds 6.Dwayne weighs two-thirds as much as his older sister. The sum of their weights is 90 lbs. How much does Dwayne weigh? D = S Since Dwayne weighs two-thirds as much as his sister, multiply her weight by two-thirds to his sister, multiply her weight by two-thirds to obtain Dwaynes weight. obtain Dwaynes weight. Dwayne weighs 36 pounds. 2 3 D = (54) 2 3 Substitute D = 36