Equations Practice Precalc

Practice Questions on solving equations Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places. 1) 2x4 - 5x2 + 7x = 14 A) {-2.32, 1.70}

2) -x4 + 3x3 +

1) B) {-2.30, 1.69}

C) {-2.31, 1.70}

D) {-2.31, 1.69}

4 2 9 x = x+2 3 2

2)

A) {-3.34}

B) no solution

C) {1.09, -0.44}

D) {2.82, 1.61, -0.46, -0.97}

Solve the equation algebraically. Verify your solution with a graphing utility. 3) 4(2x - 4) = 7(x + 3) A) {9}

3) B) {37}

C) {-37}

1

D) {-5}

4) -7x + 3 + 6(x + 1) = -2x - 6 9 A) 10

B) - 15

5) (x + 5)(x - 1) = (x + 1)2 A) {6}

6) 1 -

3 C) 8

B)

6 5

C)

5 2

4) D) {-2}

5) D) 3

6 1 = 7x 2

A) -

12 7

7) 4x2 = 2 - 2x 1 A) - , - 1 2

6) 12 7

B) - 18

C)

1 B) - , 1 2

1 ,-1 C) 2

2

D)

2 3

1 ,1 D) 2

7)

8) x3 + 4x2 - 9x - 36 = 0 A) {-3, 3, -4}

8) B) {3, -4}

C) {-3, 3, 4}

D) {9, -4}

Solve the equation. 9 5 = 9) 2x - 2 x + 5 A) {-55}

10)

B) {55}

C) {40}

D) {-35}

5 6 35 = x - 7 x - 14 (x - 7)(x - 14)

A) {14}

11)

9)

10)

B) {7}

C) {7, 14}

D) no solution

-3 -2 -3 = x - 1 x - 2 (x - 1)(x - 2)

A) {1, 2}

11) B) {2}

C) {1}

3

D) no solution

12) x = 11

12)

A) {-11, 11}

13) 3 - 5x = 6 1 11 A) - , 3 3

14) u + 9 = A) -

B) {121}

C) {-11}

D) {11}

3 9 B) - , 5 5

9 3 C) - , 5 5

11 1 , D) 3 3

1 2

17 2

14) B) -

19 2

C) -

19 17 ,2 2

D) no real solution

15) x2 + 9x - 5 = 5 A) {-10, 10, -1, 1}

13)

15) B) {-10, -9, 0, 1}

C) {-9, -1, 0, 10}

4

D) {-10, -9, 1}

Find the real solutions, if any, of the equation. Use the quadratic formula. 16) x2 + 4x - 3 = 0 A) {2 +

16)

7}

C) {-2 - 1 7, -2 + 1 7}

17) 2x2 - x + 9 = 0 -1 - 73 1 + 73 , A) 4 4 C)

18) 5 +

B) {-2 -

7, -2 +

7}

D) {-1 -

7, -1 +

7}

17)

-1 + 73 1 + 73 , B) 4 4

-1 - 73 -1 + 73 , 4 4

D) no real solution

10 3 + =0 x x2

A) C)

18)

-5 - 10 -5 + 10 , 10 10 5-

5

10 5 + ,

5

B)

10

-5 - 10 -5 + 10 , 5 5

D) no real solution

5

19) 4x = 1 + A) C)

-6 x

11-

8 8

19)

97 97 1 + ,

B) -

8

97

1+

8

97 1 ,

8

97

D) no real solution

Find the real solutions of the equation. 20) x4 - 22x2 - 75 = 0 A) {-25, 3}

20) C) {- 3,

B) {-5, 5}

3}

D) no real solution

21) x6 + 26x3 - 27 = 0 A) {-3, 1}

21) B) {27}

C) {3, -1}

D) {3}

22) (x - 4)2 + 3(x - 4) - 18 = 0 A) {-6, 1}

22) B) {-1, 6}

C) {-7, 2}

6

D) {-2, 7}