Intermediate algebra questions on various topics , with answers, are presented. The answers are at the bottom of the page. Also included are the solutions with full explanations.

1. Write 230,000,000,000 in scientific notation.

2. Evaluate: 30 - 12÷3×2 =

3. Evaluate: |4 - 8(3 - 12)| - |5 - 11| =

4. Evaluate: -18 + 4(6 ÷ 2)²

5. Evaluate: 11 + sqrt(-4 + 6×4÷3)

6. Simplify: 12x³ - 3(2x³ + 4x -1) - 5x + 7

7. Simplify: (x⁴ / x³)³

8. Simplify: (3x²y^-2)³ / (9xy³)³

9. Simplify: (2x^-3y⁴)³(x³ + y)⁰ / (4xy^-2)³

10. Write as a mathematical inequality:"9 is less than the product of M and N".

11. Find the slope of the line perpendicular to the line y = (1/3)x - 7

12. Write an equation of the line with slope -3 and y-intercept (0 , -5).

13. Solve the equation: -5x + 20 = 25

14. Solve the inequality: -3x + 4 < -8

15. Solve the equation: 2x² - 32 = 0

16. Solve the equation: -0.25 x + 1.3 = -0.55 x - 0.2

17. Solve the equation: -0.25 x² + 1.5 = -10.75

18. What is the slope of a line perpendicular to the line x = -3?

19. What is the slope of a line parallel to the line x = 5?

20. What is the slope of a line perpendicular to the line y = 6?

1. 2.3 × 10¹¹
2. 22
3. 70
4. 18
5. 13
   
   
6. 6x³ -17x + 10
7. x³
8. (1/27)(x³ / y¹⁵)
9. (1/8)(y¹⁸ / x¹²)
10. 9 < M × N
    
    
11. -3
12. y = -3x - 5
13. -1
14. x > 4
15. -4 , 4
    
    
16. -5
17. -7 , 7
18. 0
19. undefined
20. undefined