All Inequalities, GCF/LCM, Simplify Sq Rt Test

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Examples include: x > 5, y ≤ 10.

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What does GCF stand for and what does it mean?

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GCF stands for Greatest Common Factor. It is the largest positive integer that divides each of the given integers without leaving a remainder.

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What does LCM stand for and what does it mean?

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LCM stands for Least Common Multiple. It is the smallest positive integer that is a multiple of two or more integers.

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How do you solve the inequality 2(x + 4) ≤ 10?

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First, distribute: 2x + 8 ≤ 10. Then, subtract 8 from both sides: 2x ≤ 2. Finally, divide by 2: x ≤ 1.

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What is the solution to the inequality 2b + 35 > -7?

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First, subtract 35 from both sides: 2b > -42. Then, divide by 2: b > -21.

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What does it mean when an equation has no solution?

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An equation has no solution when there are no values that can satisfy the equation. For example, |−2n| + 10 = −50 has no solution because the left side cannot be negative.

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What is the first step in solving the inequality -39 > n - 25?

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Add 25 to both sides: -39 + 25 > n, which simplifies to -14 > n or n < -14.

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What is the definition of a solution set in inequalities?

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A solution set is the set of all values that satisfy the inequality. For example, the solution set for x ≤ 1 is all numbers less than or equal to 1.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities use < or >, meaning the endpoints are not included. Non-strict inequalities use ≤ or ≥, meaning the endpoints are included.