Advanced Algebra Concepts for 7th Grade

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What is the distributive property of multiplication over addition?
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The distributive property states that a(b + c) = ab + ac.
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How can you solve an equation with variables on both sides, like 2x + 5 = x + 9?
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First, subtract x from both sides to get x + 5 = 9. Then subtract 5 from both sides to get x = 4.
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What does it mean for two expressions to be equivalent?
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Two expressions are equivalent if they have the same value for all variable assignments.
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How do you simplify an expression like 3(x + 4) - 2x?
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First, use the distributive property: 3x + 12 - 2x. Then combine like terms: x + 12.
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What is the process of finding the greatest common factor (GCF) of two numbers?
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List the factors of each number, then find the largest factor that they have in common.
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How do you factor the expression x^2 + 5x + 6?
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Find two numbers that multiply to 6 and add to 5. These are 2 and 3. So, x^2 + 5x + 6 factors to (x + 2)(x + 3).
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How do you solve an equation like 4(x - 2) = 16?
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Divide both sides by 4 to get x - 2 = 4. Then add 2 to both sides to get x = 6.
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What is a linear equation?
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A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.
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How do you solve inequalities, such as 3x + 2 < 11?
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Subtract 2 from both sides to get 3x < 9, then divide by 3 to find x < 3.
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What is the commutative property of addition?
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The commutative property of addition states that the order of adding numbers does not change the sum, i.e., a + b = b + a.
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How can you express the growth of a pattern using algebra?
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Identify the relationship between variables and use an algebraic expression or equation to describe the pattern.
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What is a coefficient in an algebraic expression?
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A coefficient is a number that is multiplied by a variable in an algebraic expression, e.g., 3 in 3x.
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What does it mean for an equation to be 'solvable'?
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An equation is 'solvable' if it has a solution, meaning there is a value or values that satisfy the equation.
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How do you graph a simple linear equation like y = 2x + 3?
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Start by finding the y-intercept (0,3) and then use the slope (2, or rise over run) to plot the next point and draw the line.
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What is an algebraic expression?
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An algebraic expression is a combination of variables, numbers, and at least one operation (e.g., 3x + 2).
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