# Practice 1

Algebra Practice Problems

Click on the problem number to see the solution.

Simplify the following.

1. y = (x2)3 * x4/(x10)

2. y = x1/2* x5

3. y = 2[(x-2)2 +6x]

4. z = (x+y)2 – (x-y)2

5. y = 5a(a5)2/(a6)2

6. z = xy -2/x -2y / [x -2y3/xy -1]

7. x/(x-1) + 2/x =0

Solve each of the following for x, so that x is on the left hand side of the equation and everything else is on the right hand side.

8. xy = 10

9. 2xy + b = 4

10. x2/6 – y2/10 – 5 = 0

11. ex = 5

12. 8x = 15

13. 0.10 = ln x

14. (x+a)/b +b = a2

15. xyz – z = y2

16. x1/2/6 = 1

17. Solve for x and y: 9(x+1) + 5(y+3) = 5

7(x-3) – 3(2y+1)= -19

Use factoring to solve these problems:

18. x2 – 5x + 6 = 0

19. x4 – 2x2 = 0

20. x3ex – 27ex = 0

21. x2 +98x = 200

22. This one is already factored. What are the solutions?

ex(x2-1)/[e2xsin2x – cos(2x)] = 0

Solutions

1. y = (x2)3 * x4/(x10)

y = 1

2. y = x1/2* x5

y = x11/2

3. y = 2[(x-2)2 +6x]

y = 2x2 – 4x +32

4. z = (x+y)2 – (x-y)2

z = 4xy

5. y = 5a(a5)2/(a6)2

y = 5/a

6. z = xy -2/x -2y / [x -2y3/xy -1]

z = x6/y7

7. x/(x-1) + 2/x =0

Multiply the first term by x/x and the second term by (x-1)/(x-1). This is the same as multiplying by 1, so it doesn