Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Tell whether each equation is true, false, or open. Explain.

7. 85 + ( − 10 ) = 95 85 plus open negative 10 close equals 95
8. 225 ÷ t − 4 = 6.4 225 divides t minus 4 equals 6.4
9. 29 − 34 = − 5 29 minus 34 equals negative 5
10. − 8 ( − 2 ) − 7 = 14 − 5 negative 8 open negative 2 close minus 7 equals 14 minus 5
11. 4 ( − 4 ) ÷ ( − 8 ) 6 = − 3 + 5 ( 3 ) 4 open negative 4 close divides open negative 8 close 6 equals negative 3 plus 5 open 3 close
12. 91 ÷ ( − 7 ) − 5 = 35 ÷ 7 + 3 91 divides open negative 7 close minus 5 equals 35 divides 7 plus 3
13. 4 a − 3 b = 21 4 eh minus 3 b equals 21
14. 14 + 7 + ( − 1 ) = 21 14 plus 7 plus open negative 1 close equals 21
15. 5x + 7 = 17

See Problem 2.

Tell whether the given number is a solution of each equation.

16. 8x + 5 = 29; 3
17. 5b + 1 = 16; − 3 negative 3
18. 6 = 2 n − 8 ; 6 equals 2 n minus 8 semicolon  7
19. 2 = 10 − 4 y ; 2 equals 10 minus 4 y semicolon  2
20. 9 a − ( − 72 ) = 0 ; − 8 9 eh minus open negative 72 close equals 0 semicolon negative 8
21. − 6 b + 5 = 1 ; 1 2 negative 6 b plus 5 equals 1 semicolon , 1 half
22. 7 + 16y = 11; 1 4 1 fourth
23. 14 = 1 3 x + 5 ; 14 equals , 1 third , x plus 5 semicolon  27
24. 3 2 t + 2 = 4 ; 2 3 3 halves , t plus 2 equals 4 semicolon , 2 thirds

See Problem 3.

Write an equation for each sentence.

25. The sum of 4x and − 3 negative 3  is 8.
26. The product of 9 and the sum of 6 and x is 1.
27. Training An athlete trains for 115 min each day for as many days as possible. Write an equation that relates the number of days d that the athlete spends training when the athlete trains for 690 min.
28. Salary The manager of a restaurant earns $2.25 more each hour than the host of the restaurant. Write an equation that relates the amount h that the host earns each hour when the manager earns $11.50 each hour.

See Problem 4.

Use mental math to find the solution of each equation.

29. x − 3 = 10 x minus 3 equals 10
30. 4 = 7 − y 4 equals 7 minus y
31. 18 + d = 24
32. 2 − x = − 5 2 minus x equals negative 5
33. m 3 = 4 m over 3 , equals 4
34. x 7 = 5 x over 7 , equals 5
35. 6t = 36
36. 20a = 100
37. 13c = 26

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