True/False Algebra Questions with Answers and Explanations

Answer by true or false the following algebra questions. answers provided. Also included are the solutions with full explanations.

  1. (True or False)   \( ((2^2)^3) = 2^5 \)

  2. (True or False)   The slope of a vertical line is undefined.

  3. (True or False)   Two lines with positive slopes can be perpendicular.

  4. (True or False)   \( 5 > 10 \) or \( 5 < 7 \)

  5. (True or False)   The set of ordered pairs \(\{(6,4),(2,-5),(-2,4),(6,-4)\}\) is a function.

  6. (True or False)   The additive inverse of -10 is 10.

  7. (True or False)   The product of two positive numbers is NOT positive.

  8. (True or False)   \( x + 2 = 7 \) is called an inequality.

  9. (True or False)   The associative property is used to write \(4x + 8y = 4(x + 2y)\).

  10. (True or False)   The absolute value of a real negative number is negative.

  11. (True or False)   \( -2^3 = (-2)^3 \)

  12. (True or False)   30% of \(x\) is equal to \(0.03x\)

  13. (True or False)   "\(x\) is at most equal to 9" is written mathematically as \(x < 9\)

  14. (True or False)   \(3^{20} + 3^{20} + 3^{20} = 3^{21}\)

  15. (True or False)   \(1.5 \times 10^{-5}\) is the scientific notation of the number 0.0000015.

  16. (True or False)   \( \frac{1000}{0} = 0 \)

  17. (True or False)   \( \frac{0}{1000} = 0 \)

  18. (True or False)   \(0.0000001^0 = 1\)

  19. (True or False)   \( \frac{1}{(-2)^{-4}} = 16 \)

  20. (True or False)   \( x = 7 \) DOES NOT satisfy the inequality \(x - 7 < 0\)

Answers to the Above Questions
  1. FALSE \( (2^6) \)
  2. TRUE
  3. FALSE \( (m_1 \cdot m_2 = -1 < 0) \)
  4. TRUE
  5. FALSE (note the pairs (6,4) and (6,-4))

  6. TRUE
  7. FALSE (positive \(\times\) positive = positive)
  8. FALSE (equation)
  9. FALSE (distributive property)
  10. FALSE (positive or zero)

  11. TRUE
  12. FALSE \( (0.3x) \)
  13. FALSE \( (x \leq 9) \)
  14. TRUE
  15. FALSE (\(1.5 \times 10^{-5}\) is the scientific notation of 0.000015)

  16. FALSE (division by 0 is undefined in mathematics)
  17. TRUE
  18. TRUE
  19. TRUE
  20. TRUE

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