Intermediate Algebra True/False Questions with Answers

Answer the following true or false algebra questions designed to test your understanding of intermediate-level concepts. Click here for the solutions at the bottom of the page. You can also review the full explanations on this detailed solution page.

  1. True or False The inequality \( |x + 1| \lt 0 \) has no solution.

  2. True or False If \( a \) and \( b \) are negative numbers, and \( |a| \lt |b| \), then \( b - a \) is negative.

  3. True or False The equation \( 2x + 7 = 2(x + 5) \) has one solution.

  4. True or False The multiplicative inverse of \( -\frac{1}{4} \) is \( -\frac{1}{8} \).

  5. True or False \( \frac{x}{2 + z} = \frac{x}{2} + \frac{x}{z} \)

  6. True or False \( |-8| - |10| = -18 \)

  7. True or False \( \left( \frac{8}{4} \right) \div 2 = \frac{8}{(4 \div 2)} \)

  8. True or False \( 31.5(1.004)^{20} \lt 31.6(1.003)^{25} \)

  9. True or False The graph of the equation \( y = 4 \) has no x-intercept.

  10. True or False The value of \( \frac{n(n + 3)}{2} = \frac{3}{2} \) when \( n = 0 \).

  11. True or False The distance between the numbers -9 and 20 is equal to the distance between 9 and -20 on the number line.

  12. True or False If \( f(x) = \sqrt{1 - x} \), then \( f(-3) = 2 \).

  13. True or False The slope of the line \( 2x + 2y = 2 \) is equal to 2.

  14. True or False \( |x + 5| \) is always positive.

  15. True or False The distance between the points \( (0 , 0) \) and \( (5 , 0) \) in a rectangular system of axes is 5.

  16. True or False \( \frac{1}{2x - 4} \) is undefined when \( x = -4 \).

  17. True or False \( \left( -\frac{1}{5} \right)^{-2} = 25 \)

  18. True or False The reciprocal of 0 is equal to 0.

  19. True or False The additive inverse of -10 is equal to 10.

  20. True or False \( \frac{1}{x - 4} = \frac{1}{x} - \frac{1}{4} \)

Solutions to the Above Questions

  1. TRUE
    An absolute value is always ≥ 0, so it can never be less than 0.

  2. TRUE
    Since both are negative, \( b \lt a \), so \( b - a \lt 0 \).

  3. FALSE
    Simplifies to \( 2x + 7 = 2x + 10 \), which leads to \( 7 = 10 \), a contradiction. No solution.

  4. FALSE
    The multiplicative inverse of \( a \) is \( \frac{1}{a} \). So \( \frac{1}{-\frac{1}{4}} = -4 \).

  5. FALSE
    Test with \( x = 8 \), \( z = 2 \): LHS = \( \frac{8}{4} = 2 \); RHS = \( \frac{8}{2} + \frac{8}{2} = 4 + 4 = 8 \).

  6. FALSE
    LHS = \( 8 - 10 = -2 \), not -18.

  7. FALSE
    LHS = \( 2 \div 2 = 1 \); RHS = \( \frac{8}{2} = 4 \)

  8. FALSE
    Approximate values: LHS ≈ 34.1, RHS ≈ 33.4, so LHS > RHS.

  9. TRUE
    It's a horizontal line that never crosses the x-axis.

  10. True or False \( \frac{n(n + 3)}{2} = \frac{3}{2} \) when \( n = 0 \).
    FALSE
    Substitute \( n = 0 \): LHS = 0, not \( \frac{3}{2} \).

  11. TRUE
    Both are \( |20 - (-9)| = 29 \) and \( |9 - (-20)| = 29 \).

  12. TRUE
    \( f(-3) = \sqrt{1 - (-3)} = \sqrt{4} = 2 \).

  13. FALSE
    Rewriting: \( y = -x + 1 \), slope is -1, not 2.

  14. FALSE
    It equals 0 when \( x = -5 \).

  15. TRUE
    On the x-axis: \( \sqrt{(5 - 0)^2} = 5 \).

  16. FALSE
    It's undefined when \( 2x - 4 = 0 \Rightarrow x = 2 \).

  17. TRUE
    \( a^{-2} = \frac{1}{a^2} \), so \( (-1/5)^{-2} = \frac{1}{(1/25)} = 25 \).

  18. FALSE
    Reciprocal of 0 is undefined.

  19. TRUE
    The additive inverse of \( a \) is the number that gives 0 when added to \( a \).

  20. FALSE
    Try \( x = 2 \): LHS = \( \frac{1}{-2} \), RHS = \( \frac{1}{2} - \frac{1}{4} = \frac{1}{4} \).

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