Algebra Practice Problems
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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
