Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each equation. Check your answer.

11. 2 + a 4 = − 1 2 plus , eh over 4 , equals negative 1
12. 3 n − 4 = 11 3 n minus 4 equals 11
13. − 1 = 7 + 8 x negative 1 equals 7 plus 8 x
14. y 5 + 2 = − 8 y over 5 , plus 2 equals negative 8
15. 4 b + 6 = − 2 4 b plus 6 equals negative 2
16. 10 = x 4 − 8 10 equals , x over 4 , minus 8
17. 10 + h 3 = 1 10 plus , h over 3 , equals 1
18. − 14 = − 5 + 3 c negative 14 equals negative 5 plus 3 c
19. 26 = m 6 + 5 26 equals , m over 6 , plus 5
20. a 5 − 18 = 2 eh over 5 , minus 18 equals 2
21. − 5 x − 2 = 13 negative 5 x minus 2 equals 13
22. 14 = − 2 k + 3 14 equals negative 2 k plus 3

See Problem 2.

Define a variable and write an equation for each situation. Then solve.

23. Maximum Capacity A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. How many boxes of books can the delivery person bring up at one time?
24. Shopping You have $16 and a coupon for a $5 discount at a local supermarket. A bottle of olive oil costs $7. How many bottles of olive oil can you buy?
25. Rentals Two college friends rent an apartment. They have to pay the landlord two months’ rent and a $500 security deposit when they sign the lease. The total amount they pay the landlord is $2800. What is the rent for one month?

See Problem 3.

Solve each equation. Check your answer.

26. y − 4 2 = 10 fraction y minus 4 , over 2 end fraction . equals 10
27. 7 = x − 8 3 7 equals . fraction x minus 8 , over 3 end fraction
28. z + 10 9 = 2 fraction z plus 10 , over 9 end fraction . equals 2
29. 4 = a + 10 2 4 equals . fraction eh plus 10 , over 2 end fraction
30. 7 1 2 = x + 3 2 7 , and 1 half , equals . fraction x plus 3 , over 2 end fraction
31. b + 3 5 = − 1 fraction b plus 3 , over 5 end fraction . equals negative 1
32. − 2 = d − 7 7 negative 2 equals . fraction d minus 7 , over 7 end fraction
33. g − 3 3 = 5 3 fraction g minus 3 , over 3 end fraction . equals , 5 thirds

See Problem 4.

Solve each equation. Justify each step.

34. 14 − b = 19 14 minus b equals 19
35. 20 − 3 h = 2 20 minus 3 h equals 2
36. 3 − x 2 = 6 3 minus , x over 2 , equals 6
37. − 1 = 4 + x 3 negative 1 equals 4 plus , x over 3

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