Grade 9 ratio algebra questions with answers are presented. Questions on solving linear and quadratic equations, simplifying expressions including expressions with fractions, finding slopes of lines are included. Solutions and detailed explanations are also included.

## Questions

1. Simplify the following algebraic expressions.

1. - 6x + 5 + 12x -6
2. 2(x - 9) + 6(-x + 2) + 4x
3. 3x2 + 12 + 9x - 20 + 6x2 - x
4. (x + 2)(x + 4) + (x + 5)(-x - 1)
5. 1.2(x - 9) - 2.3(x + 4)
6. (x2y)(xy2)
7. (-x2y2)(xy2)

2. Simplify the expressions.

1. (a b2)(a3 b) / (a2 b3)
2. (21 x5) / (3 x4)
3. (6 x4)(4 y2) / [ (3 x2)(16 y) ]
4. (4x - 12) / 4
5. (-5x - 10) / (x + 2)
6. (x2 - 4x - 12) / (x2 � 2x � 24)

3. Solve for x the following linear equations.

1. 2x = 6
2. 6x - 8 = 4x + 4
3. 4(x - 2) = 2(x + 3) + 7
4. 0.1 x - 1.6 = 0.2 x + 2.3
5. - x / 5 = 2
6. (x - 4) / (- 6) = 3
7. (-3x + 1) / (x - 2) = -3
8. x / 5 + (x - 1) / 3 = 1/5

4. Find any real solutions for the following quadratic equations.

1. 2 x2 - 8 = 0
2. x2 = -5
3. 2x2 + 5x - 7 = 0
4. (x - 2)(x + 3) = 0
5. (x + 7)(x - 1) = 9
6. x(x - 6) = -9

5. Find any real solutions for the following equations.

1. x3 - 1728 = 0
2. x3 = - 64
3. sqrt(x) = -1
4. sqrt(x) = 5
5. sqrt(x/100) = 4
6. sqrt(200/x) = 2

6. Evaluate for the given values of a and b.

1. a2 + b2 , for a = 2 and b = 2
2. |2a - 3b| , for a = -3 and b = 5
3. 3a3 - 4b4 , for a = -1 and b = -2

7. Solve the following inequalities.

1. x + 3 < 0
2. x + 1 > -x + 5
3. 2(x - 2) < -(x + 7)

8. For what value of the constant k does the quadratic equation x2 +2x = - 2k have two distinct real solutions?

9. For what value of the constant b does the linear equation 2x + by = 2 have a slope equal to 2?

10. What is the y intercept of the line -4x + 6y = -12?

11. What is the x intercept of the line -3x + y = 3?

12. What is point of intersection of the lines x - y = 3 and -5x - 2y = -22?

13. For what value of the constant k does the line -4x + ky = 2 pass through the point (2,-3)?

14. What is the slope of the line with equation y - 4 = 10?

15. What is the slope of the line with equation 2x = -8?

16. Find the x and y intercepts of the line with equation x = - 3?

17. Find the x and y intercepts of the line with equation 3y - 6 = 3?

18. What is the slope of a line parallel to the x axis?

19. What is the slope of a line perpendicular to the x axis?
Solutions and detailed explanations to the above questions.

## Answers to the Above Questions

1. 6x - 1
2. - 6
3. 9x 2 + 8 x - 8
4. 3
5. -1.1x - 20
6. x3y3
7. - x3y4

1. a2
2. 7x
3. (1/2)x2y
4. x - 3
5. -5
6. (x + 2)/(x + 4)

1. x = 3
2. x = 6
3. x = 21/2
4. x = -39
5. x = -10
6. x = -14
7. no solution
8. x = 1

1. solution set {-2,2}
2. no real solutions
3. solution set {1,-7/2}
4. solution set {2,-3}
5. solution set {2,-8}
6. solution set {3}

1. x = 12
2. x = -4
3. no solutions
4. x = 25
5. x = 1600
6. x = 50

1. Evaluate for the given values of a and b.

1. 8
2. 21
3. -67

1. x < -3
2. x > 2
3. x < -1

2. k < 1/2

3. b = -1

4. (0 , -2)

5. (-1 , 0)

6. (4 , 1)

7. k = -10/3

8. slope = 0

9. The slope is undefined

10. x - intercept: (-3,0) , no y - intercept.

11. no x - intercept , y - intercept: (0 , 3)

12. slope = 0

13. The slope is undefined.