Intermediate Algebra Questions and Answers
Lines, Equations, Systems, Expressions, Factoring

This set of intermediate algebra questions covers essential topics such as lines and slopes, evaluating expressions, solving linear equations, and systems of equations. Answers are provided, at the bottom of the page, for quick checking, and for detailed step-by-step solutions and explanations, visit the fully explained step-by-step solutions.

  1. Write \( 1.5 \times 10^{-5} \) in standard form.
  2. Evaluate: \( 30 - |-x + 6| \) for \( x = 10 \)
  3. Evaluate: \( 2xy^3 + x - 2y \) for \( x = 2 \) and \( y = -2 \)
  4. What is the slope of the line perpendicular to the line \( y = -4 \)?
  5. Write an equation of the line with slope 2 and x-intercept \( (-4, 0) \).
  6. Solve the equation: \( -3(-x + 5) + 20 = -10(x - 3) + 4 \)
  7. Solve the inequality: \( 4(x - 6) + 4 < 8(x - 4) \)
  8. Solve the equation: \( 3(x - 2)^2 - 12 = 0 \)
  9. Solve the equation: \( \frac{x}{3} + \frac{2}{7} = \frac{x}{7} - 5 \)
  10. Line \( L \) is defined as the line through the point \( (2, 7) \) and perpendicular to the line \( x + y = 0 \). What is the point of intersection of \( L \) and the line \( x + y = 0 \)?
  11. What is the point of intersection of the lines: \( x + 2y = 4 \) and \( -x - 3y = -7 \)?
  12. How many solutions do the system of equations \( 2x - 3y = 4 \) and \( 4x - 6y = -7 \) have?
  13. For what value(s) of \( A \) does the system of equations \( Ax + 6y = 0 \) and \( 2x - 7y = 3 \) have no solutions?
  14. Solve \( |2x - 4| - 2 = 6 \)
  15. How many solutions does the equation \( 2x^2 + 3x = 8 \) have?
  16. Solve the equation \( 3x^2 + 6x - 1 = 8 \)
  17. Solve the system of equations: \( 2x + 5y = 18 \) and \( -3x - y = -1 \)
  18. What is the range of the function \( f \) defined by: \( f = \{(2,3), (1,4), (5,4), (0,3)\} \)
  19. Factor the expression \( 2x^2 + 3x + 1 \)
  20. Factor the expression \( 10x^2 + 20x - 80 \)

Answers to the Above Questions
  1. \( 0.000015 \)
  2. \( 26 \)
  3. \( -26 \)
  4. undefined (vertical line)
  5. \( y = 2x + 8 \)

  6. \( \frac{29}{13} \)
  7. \( x > 3 \)
  8. \( \{ 0, 4 \} \)
  9. \( -\frac{111}{4} \)
  10. \( \left( -\frac{5}{2}, \frac{5}{2} \right) \)

  11. \( (-2, 3) \)
  12. no solutions
  13. \( -\frac{12}{7} \)
  14. \( \{ -2, 6 \} \)
  15. 2 real solutions

  16. \( \{ -3, 1 \} \)
  17. \( (-1, 4) \)
  18. \( \{ 3, 4 \} \)
  19. \( (2x + 1)(x + 1) \)
  20. \( 10(x - 2)(x + 4) \)

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