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

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What does it mean if an equation has 'No Solution'?

Back

It means that there are no values for the variable that can satisfy the equation. For example, the equation 2x + 3 ≤ 4x - 2x + 1 has no solution.

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What does it mean if an equation has 'All Real Numbers' as a solution?

Back

It means that any real number can satisfy the equation, indicating infinite solutions.

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Back

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What is the solution to the equation: 3(2e + 5) + 8(1 - e) = 1?

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The solution is 11.

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Solve for x: 47 = 2x + 3(5x - 7)

Back

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What does it mean to solve an inequality?

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To find the range of values for the variable that makes the inequality true.

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Solve the inequality: 4(2a + 3) < 3(a - 1)

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The solution is @@(- ext{∞}, -3)@@.

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What is a multi-step equation?

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An equation that requires more than one step to solve, often involving combining like terms and using inverse operations.

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What is the first step in solving the equation 2x + 3 = 7?

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Subtract 3 from both sides to isolate the term with the variable.

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What is the distributive property?

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The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a parenthesis.