Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Solve each equation. Check your solutions.

8. 1 2 + 2 x = 1 x 1 half , plus , 2 over x , equals , 1 over x
9. 5 + 2 p = 17 p 5 plus , 2 over p , equals , 17 over p
10. 3 a − 5 a = 2 3 over eh , minus , 5 over eh , equals 2
11. y − 6 y = 5 y minus , 6 over y , equals 5
12. 5 2 s + 3 4 = 9 4 s fraction 5 , over 2 s end fraction , plus , 3 fourths , equals , fraction 9 , over 4 s end fraction
13. 7 + 3 x = 7 x + 9 7 plus , 3 over x , equals , 7 over x , plus 9
14. 2 c − 2 = 2 − 4 c fraction 2 , over c minus 2 end fraction . equals 2 minus , 4 over c
15. 5 3 p + 2 3 = 5 + p 2 p fraction 5 , over 3 p end fraction , plus , 2 thirds , equals . fraction 5 plus p , over 2 p end fraction
16. 8 x + 3 = 1 x + 1 fraction 8 , over x plus 3 end fraction . equals , 1 over x , plus 1
17. 1 t − 2 = t 8 fraction 1 , over t minus 2 end fraction . equals , t over 8
18. v + 2 v + 4 3 v = 11 fraction v plus 2 , over v end fraction . plus , fraction 4 , over 3 v end fraction , equals 11
19. 4 3 ( c + 4 ) + 1 = 2 c c + 4 fraction 4 , over 3 . open , c plus 4 , close end fraction . plus 1 equals . fraction 2 c , over c plus 4 end fraction
20. 3 + a 2 a = 1 3 + 5 6 a fraction 3 plus eh , over 2 eh end fraction . equals , 1 third , plus , fraction 5 , over 6 eh end fraction
21. a a + 3 = 2 a a − 3 − 1 fraction eh , over eh plus 3 end fraction . equals . fraction 2 eh , over eh minus 3 end fraction . minus 1
22. z z + 2 − 1 z = 1 fraction z , over z plus 2 end fraction . minus , 1 over z , equals 1

    See Problem 3.

23. Gardening Marian can weed a garden in 3 h. Robin can weed the same garden in 4 h. If they work together, how long will the weeding take them?
24. Trucking David can unload a delivery truck in 20 min. Allie can unload the same delivery truck in 35 min. If they work together, how long will the unloading take?

See Problems 4 and 5.

Solve each equation. Check your solutions. If there is no solution, write no solution.

25. 5 x + 1 = x + 2 x + 1 fraction 5 , over x plus 1 end fraction . equals . fraction x plus 2 , over x plus 1 end fraction
26. 4 c + 4 = c c + 25 fraction 4 , over c plus 4 end fraction . equals . fraction c , over c plus 25 end fraction
27. 3 m − 1 = 2 m m + 4 fraction 3 , over m minus 1 end fraction . equals . fraction 2 m , over m plus 4 end fraction
28. 2 x + 4 x − 3 = 3 x x − 3 fraction 2 x plus 4 , over x minus 3 end fraction . equals . fraction 3 x , over x minus 3 end fraction
29. 30 x + 3 = 30 x − 3 fraction 30 , over x plus 3 end fraction . equals . fraction 30 , over x minus 3 end fraction
30. x + 2 x + 4 = x − 2 x − 1 fraction x plus 2 , over x plus 4 end fraction . equals . fraction x minus 2 , over x minus 1 end fraction

B Apply

31. Writing How could you use cross products to solve 1 x − 2 = 2 x − 6 x + 6 + 1 ? fraction 1 , over x minus 2 end fraction . equals . fraction 2 x minus 6 , over x plus 6 end fraction . plus 1 . question mark
32. Open-Ended Write a rational equation that has 5 as a solution.

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