Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each equation. Check each solution.

8. 1 4 − x = x 8 1 fourth , minus x equals , x over 8
9. y 5 + y 2 = 7 y over 5 , plus , y over 2 , equals 7
10. 2 x 3 − 1 2 = 2 x + 5 6 fraction 2 x , over 3 end fraction , minus , 1 half , equals . fraction 2 x plus 5 , over 6 end fraction
11. 3 x − 2 12 − 1 6 = 1 6 fraction 3 x minus 2 , over 12 end fraction . minus , 1 sixth , equals , 1 sixth
12. 1 x + x 2 = x + 4 2 x 1 over x , plus , x over 2 , equals . fraction x plus 4 , over 2 x end fraction
13. 11 3 x − 1 3 = − 4 x 2 fraction 11 , over 3 x end fraction , minus , 1 third , equals . fraction negative 4 , over x squared end fraction
14. 3 2 x − 5 3 x = 2 fraction 3 , over 2 x end fraction , minus , fraction 5 , over 3 x end fraction , equals 2
15. 5 x 4 − 3 x = 1 4 fraction 5 x , over 4 end fraction , minus , 3 over x , equals , 1 fourth
16. 2 y + 1 2 = 5 2 y 2 over y , plus , 1 half , equals , fraction 5 , over 2 y end fraction
17. x + 6 x = − 5 x plus , 6 over x , equals negative 5
18. 1 4 x − 3 4 = 7 x fraction 1 , over 4 x end fraction , minus , 3 fourths , equals , 7 over x
19. 5 2 x − 2 3 = 1 x + 5 6 fraction 5 , over 2 x end fraction , minus , 2 thirds , equals , 1 over x , plus , 5 sixths

    See Problem 2.

20. Transportation The speed s of an airplane is given by s = d t , s equals , d over t , comma  where d represents the distance and t is the time.

    1. A plane flies 700 miles from New York to Chicago at a speed of 360 mi/h. Find the time for the trip.
    2. On the return trip from Chicago to New York, a tail wind helps the plane move faster. The total flying time for the round trip is 3.5 h. Find the speed x of the tail wind.

See Problem 3.

Graphing Calculator Solve each equation. Check each solution.

21. 3 x = 5 3 over x , equals 5
22. 1 3 x = − 2 fraction 1 , over 3 x end fraction , equals negative 2
23. 2 x − 1 = 4 fraction 2 , over x minus 1 end fraction . equals 4
24. 4 x + 3 = 5 fraction 4 , over x plus 3 end fraction . equals 5
25. 5 x − 2 x − 4 = − 3 fraction 5 x minus 2 , over x minus 4 end fraction . equals negative 3
26. 3 x − 1 x + 2 = 7 fraction 3 x minus 1 , over x plus 2 end fraction . equals 7
27. 2 x = x 2 2 over x , equals , x over 2
28. 2 x + 3 = x − 3 2 fraction 2 , over x plus 3 end fraction . equals . fraction x minus 3 , over 2 end fraction
29. 2 x − 1 + 3 x + 1 = 4 fraction 2 , over x minus 1 end fraction . plus . fraction 3 , over x plus 1 end fraction . equals 4

B Apply

Solve each equation for the given variable.

30. m = 2 E V 2 ; E m equals . fraction 2 e , over v squared end fraction . semicolon e
31. c E − 1 m c = 0 ; E c over e , minus , fraction 1 , over m c end fraction , equals 0 semicolon e
32. m F = 1 a ; F m over f , equals , 1 over eh , semicolon f
33. 1 c − c a 2 − b 2 = 0 ; c 1 over c , minus . fraction c , over eh squared , minus , b squared end fraction . equals 0 semicolon c
34. l T 2 = g 4 π 2 ; T fraction l , over t squared end fraction , equals . fraction g , over 4 , pi squared end fraction . semicolon t
35. q m = 2 V B 2 r 2 ; B q over m , equals . fraction 2 v , over b squared , r squared end fraction . semicolon b
36. Think About a Plan You and a classmate have volunteered to contact every member of your class by phone to inform them of an upcoming event. You can complete the calls in six days if you work alone. Your classmate can complete them in four days. How long will it take to complete the calls working together?
    • If N is the total number of calls, what expression represents the number of calls that you can make per day? What expression represents the number of calls your friend can make per day?
    • What is the expression for the number of days needed to make N calls if you are working together?
37. Storage One pump can fill a tank with oil in 4 hours. A second pump can fill the same tank in 3 hours. If both pumps are used at the same time, how long will they take to fill the tank?

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