M1. Pre Mod 4 Solving Multi-Step Equations & Inequalities

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What is a multi-step equation?

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A multi-step equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

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What does it mean if an equation has no solution?

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An equation has no solution when there are no values for the variable that make the equation true. This often occurs when simplifying leads to a false statement, such as 0 = 5.

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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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How do you determine if an equation has infinitely many solutions?

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An equation has infinitely many solutions when both sides simplify to the same expression, indicating that any value for the variable will satisfy the equation.

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥, indicating that one expression is less than or greater than the other.

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How do you solve an inequality?

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To solve an inequality, isolate the variable on one side using inverse operations, similar to solving an equation. Remember to reverse the inequality sign when multiplying or dividing by a negative number.

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What does it mean to simplify an equation?

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Simplifying an equation involves combining like terms and reducing the equation to its simplest form, making it easier to solve.

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What is the solution set of an inequality?

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The solution set of an inequality is the set of all values that satisfy the inequality. It can be represented in interval notation or on a number line.

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What is the difference between a solution and a root of an equation?

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A solution of an equation is a value that makes the equation true, while a root specifically refers to the value of the variable that makes a polynomial equation equal to zero.

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How do you check if your solution to an equation is correct?

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To check if your solution is correct, substitute the solution back into the original equation and verify that both sides are equal.