Justifying Solution to linear Equations in one variable.

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What is the Distributive Property?

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The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

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What does it mean if an equation has One Solution?

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An equation has One Solution if there is exactly one value of the variable that makes the equation true.

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What is the Addition Property of Equality?

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The Addition Property of Equality states that if you add the same number to both sides of an equation, the two sides remain equal.

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What does it mean if an equation has Infinite Solutions?

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An equation has Infinite Solutions if any value of the variable makes the equation true, often resulting in a tautology like x = x.

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What does it mean if an equation has No Solution?

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An equation has No Solution if there is no value of the variable that can make the equation true, often resulting in a contradiction like 5 = 3.

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What is the Commutative Property?

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The Commutative Property states that the order in which you add or multiply numbers does not change the result. For example, a + b = b + a.

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What is the Identity Property of Addition?

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The Identity Property of Addition states that adding zero to any number does not change the number. For example, a + 0 = a.

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What is the Identity Property of Multiplication?

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The Identity Property of Multiplication states that multiplying any number by one does not change the number. For example, a × 1 = a.

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What is the Associative Property?

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The Associative Property states that the way in which numbers are grouped when adding or multiplying does not change the result. For example, (a + b) + c = a + (b + c).

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What is the Subtraction Property of Equality?

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The Subtraction Property of Equality states that if you subtract the same number from both sides of an equation, the two sides remain equal.