Core algebra rules, equation solving, and inequality concepts tested on the GRE quantitative reasoning section.
34 cards · basic cards · AI-written, checked twice. Edit anything.
- What does the commutative property of addition state?
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a + b = b + a (order does not matter)- What does the commutative property of multiplication state?
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a × b = b × a (order does not matter)- What does the associative property of addition state?
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(a + b) + c = a + (b + c) (grouping does not matter)- What does the associative property of multiplication state?
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(a × b) × c = a × (b × c) (grouping does not matter)- State the distributive property.
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a(b + c) = ab + ac and a(b - c) = ab - ac- If a = b, what operations preserve the equality?
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Add or subtract the same number from both sides- If a = b, what other operation preserves equality?
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Multiply or divide both sides by the same nonzero number- When you multiply or divide both sides of an inequality by a negative number, what must you do?
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Flip the inequality sign (reverse its direction)- How do you interpret a compound inequality written as a < x < b?
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x is greater than a AND x is less than b (both conditions must be true)- Solve |x| = 5. What are the solutions?
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x = 5 or x = -5- Solve |x| < 3. Describe the solution set.
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-3 < x < 3- Solve |x| > 2. Describe the solution set.
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x < -2 or x > 2- Factor (a + b)(a - b). What is the result?
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a^2 - b^2- Expand (a + b)^2. What is the result?
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a^2 + 2ab + b^2- State the quadratic formula for solving ax^2 + bx + c = 0.
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x = (-b ± sqrt(b^2 - 4ac)) / (2a)
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