Calculus Homework Algebra Practice Problems for Precalculus and Calculus Solve the following equations for the unknown x : 1. 5 = 7x 16 2. 2x

Calculus Homework

Algebra Practice Problems for Precalculus and Calculus

Don't use plagiarized sources. Get Your Custom Assignment on
Calculus Homework Algebra Practice Problems for Precalculus and Calculus Solve the following equations for the unknown x : 1. 5 = 7x 16 2. 2x
From as Little as $13/Page

Solve the following equations for the unknown x :

1. 5 = 7x 16

2. 2x 3 = 5 x

3. 12 (x 3) + x = 17 + 3(4 x )

4. 5x =
2

x 3

Multiply the indicated polynomials and simplify.

5. (4x 1)(3x + 2)

6. (x 1)(x 2 + x + 1)

7. (x + 1)(x 2 x + 1)

8. (x 2)(x + 2)

9. (x 2)(x 2)

10. (x 3 + 2x 1)(x 3 5x 2 + 4)

Find the domain of each of the following functions in 11-15.

11. f (x ) =

1 + x

12. f (x ) = 11+x

13. f (x ) = 1
x

14. f (x ) = 1
1+x

15. f (x ) = 1
1+x 2

16. Given that f (x ) = x 2 3x + 4, find and simplify f (3), f (a), f (t ), and f (x 2 + 1).

Factor the following quadratics

17. x 2 x 20

18. x 2 10x + 21

19. x 2 + 10x + 16

20. x 2 + 8x 105

21. 4x 2 + 11x 3

22. 2x 2 + 7x + 15

23. x 2 2

1

Solve the following quadratic equations in three ways: 1) factor, 2) quadratic formula, 3) complete the square

24. x 2 + 6x 16 = 0

25. x 2 3x 2 = 0

26. 2x 2 + 2x 4 = 0

Solve the following smorgasbord of equations and inequalities

27.

x =

2x 1

28.

x 2 3 =

2x

29. |x 5| = 4

30. 2x + 4 3

31. 2x + 4 3

32. x +4x 3 = 2

33. x 2 x 2 > 0

Add/Subtract the following rational expressions:

34. xx +2 +
3

x 4

35. x
2+1

(x 1)(x 2)
x 3

x 3

Simplify the following rational expressions (if possible):

36. x
2+x 2
x 21

37. x
2+5x +6

x 23x +2

38.

x
x +2 + 3

x +1
x 1

Solutions

1. Given that 5 = 7x 16, add 16 to both sides to get 7x = 21. Now divide both sides by 7 to get x = 3. Checking, we see that
7(3) 16 = 21 16 = 5.

2. Given that 2x 3 = 5 x , add x to both sides and then add 3 to both sides to get 3x = 8. Now divide both sides by 3 to get
x = 8/3 = 2.6. Checking, we see that 2(8/3) 3 = 163 3 =

16
3

9
3 =

7
3 and 5 (8/3) =

15
3

8
3 =

7
3 .

3. Given that 12 (x 3) + x = 17 + 3(4 x ), we first simplify the left and right hand sides using the distributive property to get
1
2 x

3
2 + x = 17 + 12 3x . Combining like terms on both sides gives

3
2 x

3
2 = 29 3x . Now we add 3x and

3
2 to both

sides, obtaining 92 x =
61
2 . Dividing both sides by

9
2 (or multiplying both sides by

2
9 ) gives x =

61
2

2
9 =

61
9 . Checking we see

that L H S = 12 (
61
9

27
9 ) +

61
9 =

1
2

34
9 +

61
9 =

17
9 +

61
9 =

78
9 and R H S = 17 + 3(

36
9

61
9 ) = 17 + 3

(

25
9

)

= 17 759 =
153

9
75
9 =

78
9 .

2