# Twenty Algebra Questions

Algebra Questions. See attached file for full problem description.

1. Solve 15x = 2x2 + 16

2. The width is 7 feet less than the length; the area is 18 square feet. Find the length and width.

3. Solve x2 + 4x - 12 < 0

4. Solve (x + 3)/(x - 4) < 0

5. Find f(-13) for f(x) = third root of (2x - 1)

6. Rewrite (third root of (7xy))4

7. Simplify fifth root of (p14q9r23)

8. Solve third root of (3y + 6) + 2 = 5

9. Solve for t: L = (Mt + g)/t

10. Graph f(x) = |x| - 4

11. Graph f(x) = x2 - 1

12. Simplify (x3y/pq2)-3

13. Subtract and simplify 4/(5a2 - 5a) - 2/(5a - 5)

14. Find the domain of f(x) = 15/(3x - 8)

15. - 18. See file for description.

19. Solve 3(r - 6) + 2 > 4(r + 2) - 21

20. Graph 2x + 3y >= 6

#### Solution Preview

1. Solve 15x = 2x2 + 16

Put everything on one side of the equation, then use the quadratic formula:

15x = 2x2 + 16

0 = 2x2 - 15x + 16

x = 15 ±√(152 - 4(2)(16))

2(2)

x = 15 ±√97

4

x = 1.29, 6.21

2. The width is 7 feet less than the length; the area is 18 square feet. Find the length and width.

Let x be the length of the flowerbed. Then, x - 7 would be the width. Since, area is equal to length x width, we have the following equation:

(x)(x - 7) = 18

Multiply, put everything on one side of the equation, then factor to solve for x:

(x)(x - 7) = 18

x2 - 7x = 18

x2 - 7x -18 = 0

(x - 9)(x + 2) = 0

x = 9, -2

The only possible answer for x is x = 9 (a length can't be negative). Therefore, the sides are 9 and 2.

3. Solve x2 + 4x - 12 < 0

x2 + 4x - 12 < 0

(x + 6)(x - 2) < 0

This happens when x is between -6 and 2. In solution set notation, this is {x | -6 < x < 2}; in interval notation, this is (-6, 2). ...

#### Solution Summary

This problem set has twenty questions involving solving equations, simplifying expressions, exponents, roots, absolute value, graphing, and word problems.