Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each equation.

10. h − 12 = 6 h minus 12 equals 6
11. − x 3 = 27 negative , x over 3 , equals 27
12. 4 t = 48 4 t equals 48
13. 22 + r = 36 22 plus r equals 36

See Problem 2.

Solve each equation. Check your answer.

14. 7 w + 2 = 3 w + 94 7 w plus 2 equals 3 w plus 94
15. 15 − g = 23 − 2 g 15 minus g equals 23 minus 2 g
16. 43 − 3 d = d + 9 43 minus 3 d equals d plus 9
17. 5 y + 1.8 = 4 y − 3.2 5 y plus 1.8 equals 4 y minus 3.2
18. 6 a − 5 = 4 a + 2 6 eh minus 5 equals 4 eh plus 2
19. 7 y + 4 = 3 − 2 y 7 y plus 4 equals 3 minus 2 y
20. 5 c − 9 = 8 − 2 c 5 c minus 9 equals 8 minus 2 c
21. 4 y − 8 − 2 y + 5 = 0 4 y minus 8 minus 2 y plus 5 equals 0
22. 6 ( n − 4 ) = 3 n 6 open n minus 4 close equals 3 n
23. 2 − 3 ( x + 4 ) = 8 2 minus 3 open x plus 4 close equals 8
24. 5 ( 2 − g ) = 0 5 open 2 minus g close equals 0
25. 2 ( x + 4 ) = 8 2 open x plus 4 close equals 8

See Problem 3.

Write an equation to solve each problem.

26. Bus Travel Two buses leave Houston at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 45 mi\h. When will they be 400 mi apart?
27. Aviation Two planes left an airport at noon. One flew east and the other flew west at twice the speed. After 3 hours the planes were 2700 mi apart. How fast was each plane flying?
28. Geometry The length of a rectangle is 3 cm greater than its width. The perimeter is 24 cm. What are the dimensions of the rectangle?

See Problem 4.

Determine whether the equation is always, sometimes, or never true.

29. 5 x + 3 − 2 x = 7 x + 3 5 x plus 3 minus 2 x equals 7 x plus 3
30. 2(5x + 4) = 10x + 6
31. 2 3 x + 4 = 2 x 2 thirds , x plus 4 equals 2 x
32. 6 x − 12 + 2 x = 3 + 8 x − 15 6 x minus 12 plus 2 x equals 3 plus 8 x minus 15

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