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TestAlgebra 20 Flashcards 
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Card: 1 / 20 
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What is the definition of a variable in algebra? |
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Card: 2 / 20
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A variable is a symbol, typically a letter, that represents an unknown value in mathematical expressions or equations. For example, in the expression 3x + 5 = 20, x is the variable. Hint: Variables can take on different numerical values, which is crucial for solving equations. |
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Card: 3 / 20
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What is the formula for the difference of two squares? |
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Card: 4 / 20
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The formula for the difference of two squares is a² - b² = (a - b)(a + b). For example, if a = 5 and b = 3, then 5² - 3² = (5 - 3)(5 + 3) = 2 * 8 = 16. Hint: Look for expressions that fit the form of a difference of squares to apply this formula. |
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Card: 5 / 20
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What is a useful tip for solving equations with exponents? |
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Card: 6 / 20
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When solving equations with exponents, rewrite the bases in terms of their prime factors to combine like terms more easily. For example, if you have 2²x = 8, rewrite 8 as 2³ to get 2²x = 2³, which allows you to set the exponents equal: 2x = 3. Hint: Prime factorization can simplify comparisons and help isolate variables. |
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Card: 7 / 20
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If 3²x - 3² = 0, what is the value of x? |
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Card: 8 / 20
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First, factor out the common term: 3²(x - 1) = 0. Set the factor equal to zero: x - 1 = 0, leading to x = 1. Hint: Recognize that if a product equals zero, at least one factor must be zero. |
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Card: 9 / 20
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What is the quadratic formula used for? |
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Card: 10 / 20
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The quadratic formula is used to find the roots of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / 2a. For example, for the equation 2x² + 4x - 6 = 0, identify a = 2, b = 4, c = -6, and substitute into the formula. Hint: Ensure you calculate the discriminant (b² - 4ac) first to determine the nature of the roots. |
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Card: 11 / 20
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How do you solve the equation 5x - 2(3 - x) = 7? |
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Card: 12 / 20
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First, distribute the -2: 5x - 6 + 2x = 7. Combine like terms: 7x - 6 = 7. Add 6 to both sides: 7x = 13. Finally, divide by 7: x = 13/7. Hint: Always distribute carefully and combine like terms systematically to isolate the variable. |
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Card: 13 / 20
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What is the formula for squaring a binomial? |
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Card: 14 / 20
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The formula for squaring a binomial is (a ± b)² = a² ± 2ab + b². For instance, (x + 4)² = x² + 2(4)x + 16 = x² + 8x + 16. Hint: Remember to square both terms and include the middle term that is twice the product of the two terms. |
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Card: 15 / 20
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If x² + bx + 36 = 0 has two distinct integer roots, how many values can b take? |
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Card: 16 / 20
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The roots must satisfy the conditions that their product (36) and sum (-b) are integers. Possible pairs (1,36), (2,18), (3,12), (4,9), (6,6) yield sums: 37, 20, 15, 13, 12 respectively. Hence, possible b values are -37, -20, -15, -13, -12. Thus, b can take 5 distinct values. Hint: Factor pairs help determine possible sums and corresponding b values. |
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Card: 17 / 20
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What is the value of x if 2x + 3 = 11? |
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Card: 18 / 20
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Subtract 3 from both sides to get 2x = 8. Then, divide by 2 to find x = 4. Hint: Isolate the variable by performing inverse operations step by step. |
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Card: 19 / 20
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If (3x + 2)(x - 4) = 0, what are the possible values of x? |
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Card: 20 / 20
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Set each factor equal to zero: 3x + 2 = 0 gives x = -2/3 and x - 4 = 0 gives x = 4. Thus, the possible values of x are -2/3 and 4. Hint: Use the zero product property to find solutions. |
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 Completed! Keep practicing to master all of them. |
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