Free Printable Unit 6 Quiz 2 Rational Equations

1.

Solve

a)

x = 0 , 4

b)

x = 1 , 3

c)

x = -4 , 0

d)

x = 5 , 2

2.

Solve for x.

a)

2

b)

18/5

c)

26/5

d)

6

3.

a)

x = -1

b)

x = 1

c)

x = -9

d)

x = 9

4.

Solve for x

a)

x = 10

b)

x = $-\frac{30}{13}$

c)

x = 6

d)

no solution

5.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

6.

Solve and check for extraneous solutions

a)

x= - 3 &x= -8

b)

x= -3 & -8 is extraneous

c)

No Solution

d)

x= -8 & -3 is extraneous

7.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

8.

Solve for x

a)

4

b)

2

c)

-2

d)

-4

9.

Solve.

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

10.

a)

x=-12

b)

x=-18

c)

x=-3

d)

x=18

11.

a)

x = 2

b)

x = 3/4

c)

x = 4

d)

x = 1/2

12.

a)

(-2,2)

b)

$\left(-\infty,\ -2\right)\cup\left(2,\ \infty\right)$

c)

[-2,2]

d)

$\left(\infty,\ -2\right)\cup\left(2,\ -\infty\right)$

13.

a)

3/5

b)

3/4

c)

1/4

d)

4/5

14.

a)

-25/3

b)

4

c)

-6

d)

25/3

15.

a)

13/5

b)

-13/5

c)

5/13

d)

-5/13

16.

a)

5/4

b)

2/5

c)

1/3

d)

4/3

17.

a)

$\left[0,3\right)$

b)

$\left(0,3\right]$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,0\right)$

18.

a)

3/5

b)

3/4

c)

1/4

d)

4/5

19.

a)

3/4

b)

4/3

c)

2/5

d)

1/4

20.

Solve for x

a)

x = 5

b)

x = $\frac{4}{5}$

c)

x = 1

d)

x = - 4

21.

Solve

a)

k = 1, k = 5

b)

k = −1, k = 5

c)

k = −1, k = −3

d)

k = 1

22.

Solve the rational equation.

*Choose all that apply.

$\frac{x}{2x-3}=\frac{3x}{x+11}$

a)

x = 0

b)

x = -11

c)

x = 4

d)

x = -5

e)

x = 1

23.

Solve the rational equation. Answer in simplest form.

*type "no solution" when applicable

*use / when answer is a fraction

$\frac{x}{x-1}-\frac{2}{x}=\frac{1}{x-1}$

(a)

24.

Solve the rational equation.

$\frac{2}{x^2+6x+8}+\frac{5}{x^2-x-6}=\frac{x}{x^2+x-12}$

(a)

25.

Solve by cross-multiplying

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

26.

Solve by cross-multiplying.

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

27.

Solve by cross-multiplying.

a)

x = -1, 5

b)

No Solution

c)

x = -4, 5

d)

x= -4

28.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

29.

Identify the LCD.

a)

(x + 5)

b)

x²(x + 5)

c)

x

d)

x(x + 5)

30.

Solve by using the LCD.

a)

x = 4/3

b)

x = 2

c)

x = 3/4

d)

x = 2/3

31.

Solve by using the LCD.

a)

x = -2, 8

b)

x = 0, 4

c)

x = 2, -8

d)

x = 8

32.

Solve by using the LCD.

a)

x = 0, 5/2

b)

x = 5/2

c)

x = 0

d)

No Solution

33.

Solve by using the LCD.

a)

x = 1

b)

x = 2, 4

c)

x = 0, 5

d)

x = -5, -1

34.

Solve by using the LCD.

a)

x = 1

b)

x = -3

c)

x = 0

d)

x = 3

35.

The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?

a)

308.05 ft

b)

295.75 ft

c)

296.09 ft

d)

253.5 ft

36.

Patrick Mahomes can throw a football at an airspeed of 60 mph. While throwing the ball around at practice he realized he could throw the ball 80 yards with the wind at his back and only 70 yards while throwing against the wind. What was the rate of the wind?

a)

14 yph

b)

900 mph

c)

Wind does not affect Patrick Mahomes.

d)

4 mph

37.

To solve

\frac{x+12}{𝑥+2}≤2

, first, we transform the given inequality into its general form which is...

a)

$\frac{x+12}{𝑥+2}+2≤0$

b)

$\frac{x+12}{𝑥+2}-2≤0$

c)

$2\left(\frac{x+12}{𝑥+2}\right)≤0$

d)

$\frac{1}{2}\left(\frac{x+12}{𝑥+2}\right)≤0$

38.

Next, we combine the left hand side of

\frac{x+12}{𝑥+2}-2≤0

into a single rational expression which is...

a)

$\frac{x+12+2\left(x+2\right)}{𝑥+2}≤0$

b)

$\frac{x-12+2\left(x-2\right)}{𝑥+2}≤0$

c)

$\frac{x+12-2\left(x+2\right)}{𝑥+2}≤0$

d)

$\frac{x+12-2\left(x+2\right)}{𝑥-2}≤0$

39.

Then, we use distributive property of multiplication to make

\frac{x+12-2\left(x+2\right)}{𝑥+2}≤0

into...

a)

$\frac{x+12-2x+2}{𝑥+2}≤0$

b)

$\frac{x-12-2x-2}{𝑥+2}≤0$

c)

$\frac{x+12-2x+4}{𝑥+2}≤0$

d)

$\frac{x+12-2x-4}{𝑥+2}≤0$

40.

Combining like terms will simplify

\frac{x+12-2x-4}{𝑥+2}≤0

into...

a)

$\frac{x+8}{𝑥+2}≤0$

b)

$\frac{x-8}{𝑥+2}≤0$

c)

$\frac{-x+8}{𝑥+2}≤0$

d)

$\frac{-x-8}{𝑥+2}≤0$

41.

Based from

\frac{-x+8}{𝑥+2}≤0

, what are the critical values of the given rational inequality?

a)

$8\ \&\ 2$

b)

$-8\ \&\ -2$

c)

$-8\ \&\ 2$

d)

$8\ \&\ -2$

42.

Finally, using test points, what is the solution to the rational inequality

\frac{-x+8}{𝑥+2}≤0

?

a)

$\left(-\infty,\ -2\right)\cup\left[8,\ \infty\right)$

b)

$\left(-\infty,\ -2\right)$

c)

$\left[8,\ \infty\right)$

d)

$\left(-2,\ 8\right]$

43.

Solve:

\frac{x}{x^2-1}>0

a)

$\left(-1,1\right)$

b)

$\left(-1,\infty\right)$

c)

$\left(-1,0\right)\cup\left(1,\infty\right)$

d)

$\left(1,\ \infty\right)$

44.

What are the solution set of the the rational inequality

\frac{x^2+5x+6}{x^2\ -1}>0

?

a)

$\left(-\infty,-3\right)\cup\left(-2,-1\right)\cup\left(1,\infty\right)$

b)

$\left(-\infty,-6\right)\cup\left(-6,-1\right)\cup\left(1,\infty\right)$

c)

$\left(-\infty,-3\right)\cup\left(1,\infty\right)$

d)

$\left(-\infty,-6\right)\cup\left(-6,-1\right)$

45.

Solve the rational inequality and state your solution in interval notation.

$\frac{-x}{x-3}\ge0$

a)

$\left(0,\ +\infty\right)$

b)

$\left[0,\ 3\right)$

c)

$\left(-\infty,\ 0\right)\cup\left(3,\ +\infty\right)$

d)

$\left(-\infty,\ 0\right]\cup\left[3,\ +\infty\right)$

46.

Solve the rational inequality and state your solution in interval notation.

$\frac{3x-7}{x+2}>0$

a)

$\left(-2,\ \frac{7}{3}\right)$

b)

$\left(\ \frac{7}{3},\ +\infty\right)$

c)

$\left(-\infty,-2\right)\cup\left(\frac{7}{3},\ +\infty\right)$

d)

$\left(-\infty,-2\right)\cup\left[\frac{7}{3},\ +\infty\right)$

47.

Solve the rational inequality and state your solution in interval notation.

$\frac{x-1}{x^2-4}<0$

a)

$\left(-\infty,\ -2\right)$

b)

$\left(-\infty,\ -2\right)\cup\left(-2,\ 2\right)$

c)

$\left(-\infty,\ -2\right)\cup\left(1,\ 2\right)$

d)

$\left(-\infty,\ -2\right)\cup\left(-2,\ 2\right)\cup\left(2,\ +\infty\right)$

48.

A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

a)

2 hours at 105 mph
3 hours at 115 mph

b)

3 hours at 105 mph
2 hours at 115 mph

c)

1 hour at 105 mph
4 hours at 115 mph

d)

2.5 hours at 105 mph
2.5 hours at 115 mph

49.

You have 2 machines that create boxes. Working alone, machine 1 can produce 1500 boxes in x hours. But when they work together, they can cover 1500 boxes in y hours. In terms of x and y, how many hours does it take the 2nd machine by itself to produce 1500 boxes?

a)

x/(x+y)

b)

y/(x+y)

c)

xy/(x+y)

d)

xy/(x-y)

50.

Lucy and Quinn have started a car washing business. Lucy can wash a car in 3 hours. Together, Lucy and Quinn can wash a car in 1 hour. How long does it take Quinn to wash a car by herself?

a)

It takes Quinn 4 hours.

b)

It takes Quinn 2 hours.

c)

It takes Quinn 1.5 hours.

d)

I don't know. It's too cold to wash cars! *DON'T PICK THIS!*

51.

Tim can paint the football field in 8 hours. JaQuii can paint the football field in 6 hours. Damien can paint the field in 4 hours. How long does it take them to paint the field together?

a)

It will take them 24 hours.

b)

It will take them 1.8 hours.

c)

It will take them 11 hours.

d)

It will take them 2.4 hours.

52.

Divide

a)

x+8/x+4

b)

x+4/x+8

c)

16/x-4

d)

x-4/x+8

53.

Bob can mow a yard in 5 hours and Jeff can mow the same lawn in 3 hours. Which equation could be used to solve an equation to find the time it would take to mow the yard if they both mowed the lawn at the same time.

a)

$\frac{1}{3}+\frac{1}{5}+x=1$

b)

$\frac{x}{5}+\frac{1}{3}=1$

c)

$\frac{1}{5}+\frac{x}{3}=1$

d)

$\frac{x}{3}+\frac{x}{5}=1$

54.

It takes Roger 2 hours to paint a room. It takes Erin 3 hours to paint the same size of room. Which equation could be used to solve to find the time it would take to paint the room if they painted together.

a)

$\frac{1}{3}+\frac{1}{2}=6x$

b)

$\frac{x}{3}+\frac{x}{2}=6$

c)

$\frac{x}{3}+\frac{x}{2}=1$

d)

$\frac{x}{3}+\frac{x}{2}=6x$

55.

Catherine can paint a house in 15 hours. Dan can paint a house in 30 hours. How long will it take them working together.

a)

20 hours

b)

10 hours

c)

22 hours

d)

17 hours

56.

Ned made a trip to his cabin on the lake and back. The trip there took six hours and the trip back took four hours. What was Hank's average speed on the trip there if he averaged 30 km/h on the return trip?

a)

25 km/h

b)

20 km/h

c)

16 km/h

d)

10 km/hr

57.

About 13 out of 20 homes have a personal computer. On a street with 60 homes, how many would you expect to have a personal computer?

a)

7 homes

b)

39 homes

c)

73 homes

d)

40 homes

58.

Solve: $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

$\frac{5}{\left(x+5\right)\left(x-5\right)}$

d)

No Solution

59.

Simplify:

$\frac{5x}{2x-3}-\frac{4x^2}{3x+1}$

a)

no solution

b)

$\frac{-8x^3+27x^2+5x}{\left(2x-3\right)\left(3x+1\right)}$

c)

$\frac{-8x^3+3x^2+5x}{\left(2x-3\right)\left(3x+1\right)}$

d)

$\frac{7x^2+17x}{\left(2x-3\right)\left(3x+1\right)}$

60.

Simplify:

$\frac{8x}{x-4}-\frac{11}{3x+1}$

a)

$\frac{24x^2-3x-44}{\left(3x+1\right)\left(x-4\right)}$

b)

$\frac{24x^2+19x-44}{\left(3x+1\right)\left(x-4\right)}$

c)

$\frac{24x^2-3x+44}{\left(3x+1\right)\left(x-4\right)}$

d)

$\frac{13x^2+52x}{\left(3x+1\right)\left(x-4\right)}$

61.

Simplify:

$\frac{-3x}{x+5}+\frac{7}{2x-8}$

a)

$\frac{-6x^2+31x+35}{\left(x+5\right)\left(2x-8\right)}$

b)

$\frac{-6x^2-17x+35}{\left(x+5\right)\left(2x-8\right)}$

c)

$\frac{25x+35}{\left(x+5\right)\left(2x-8\right)}$

d)

$\frac{6x^2-17x+35}{\left(x+5\right)\left(2x-8\right)}$

62.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

63.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

64.

Simplify (Add & Divide)

$\frac{\frac{1}{2x}+\frac{2}{3x}}{\frac{x-1}{x-3}}$

a)

$\frac{7x-21}{6x^2-6x}\ ,\ x\ne0,\ 1,\ 3$

b)

A $\frac{7x-21}{6x^2-6x}\ ,\ x\ne1,\ 3$

c)

$\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne0\ ,\ 1,\ 3$

d)

$\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne1,\ 3$

65.

Subtract

$\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$

a)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

b)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

c)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

d)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

66.

Add

$\frac{7x}{x^2-5x}+\frac{x^2}{x-5}$

a)

$\frac{x^2+7}{x-5}\ ,\ x\ne5$

b)

$\frac{x^2+7}{x-5}\ ,\ x\ne0,\ 5$

c)

$\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)}\ ,\ x\ne5$

d)

$\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)}\ ,\ x\ne0,\ 5$

67.

Add

$\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$

a)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$

b)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$

c)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$

d)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$

68.

Add

$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$

a)

$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

b)

$\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$

c)

$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

d)

$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

69.

Add

$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ 1$

c)

$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-2,\ \frac{1}{4}$

d)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)}\ ,\ x\ne-\frac{1}{4},\ 2$

70.

Subtract

$\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$

a)

$\frac{x^2-2x-8}{2x+7}\ ,\ x\ne-\frac{7}{2}$

b)

$x^2-2x-8\ ,\ x\ne0$

c)

$x^2-2x+2\ ,\ x\ne0$

d)

$\frac{x^2-2x+2}{2x+7}\ ,\ \ x\ne-\frac{7}{2}$

71.

Add

$\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}$

a)

$\frac{4x-6}{4x-7}\ ,\ x\ne-\frac{7}{4}$

b)

$\frac{4x^2-6x+9}{4x-7}\ ,\ \ x\ne\frac{7}{4}$

c)

$\frac{4x-6}{4x-7\ }\ ,\ x\ne\frac{7}{4}$

d)

An $\frac{4x-6}{8x-14},\ x\ne\frac{14}{8}$ swer 4

72.

The number of gallons of fuel used on a trip varies directly with the number of miles traveled.
If a trip of 270 miles required 12 gallons of fuel,
how many gallons are required for a trip of 405 miles?

a)

8 gallons

b)

10 gallons

c)

17.8 gallons

d)

18 gallons

73.

a)

(-2,2)

b)

$\left(-\infty,\ -2\right)\cup\left(2,\ \infty\right)$

c)

[-2,2]

d)

$\left(\infty,\ -2\right)\cup\left(2,\ -\infty\right)$

74.

Solve for x:
$\frac{3x-7}{x+2}>1$

a)

$\left(-2,\ \frac{9}{2}\right)$

b)

$\left(-\infty,-2\right)\cup\left(\frac{9}{2},\ \infty\right)$

c)

$\left(-\infty,-2\right)\cup\left(\frac{7}{3},\ \infty\right)$

d)

$\left(-2,\ \frac{7}{3}\right)$

75.

a)

$\left[0,3\right)$

b)

$\left(0,3\right]$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,0\right)$

76.

Subtract

a)

A

b)

B

c)

C

d)

D

77.

a)

A

b)

B

c)

C

78.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

79.

a)

[-3, -1/2] [1, oo)

b)

[1,2]

c)

(-oo, -3) u (-1/2, 1)

d)

(-3, -1/2) u (1, oo)

80.

a)

(-oo, -4) u (3, oo)

b)

(-4, 3)

c)

[-4, 3]

d)

(-oo, -4] u [3, oo)

81.

a)

(-10, -2)

b)

[-10, -2]

c)

(-oo, -10] u (-2, 2)

d)

(-oo, -10) U (-2, 2]

Unit 6 Quiz 2 Rational Equations

Total questions: 81

Worksheet time: 3hrs 12mins

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