Algebra 1: Compound Inequalities and Absolute Value

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What is a compound inequality?

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A compound inequality is an inequality that combines two or more inequalities using the words 'and' or 'or'. For example, x < 5 and x > 1.

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How do you express the solution of a compound inequality in interval notation?

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The solution of a compound inequality can be expressed in interval notation by combining the intervals of the individual inequalities. For example, for x < 5 and x > 1, the interval notation is (1, 5).

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What does a closed dot on a number line represent?

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A closed dot represents that the number is included in the solution set, indicating the use of ≤ or ≥ in the inequality.

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What does an open dot on a number line represent?

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An open dot represents that the number is not included in the solution set, indicating the use of < or > in the inequality.

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How do you write the inequality -4 ≤ x < -1 in interval notation?

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The interval notation for -4 ≤ x < -1 is [-4, -1).

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What is the solution to the inequality 3x + 2 < -7?

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To solve 3x + 2 < -7, subtract 2 from both sides to get 3x < -9, then divide by 3 to find x < -3.

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What is the solution to the inequality -4x + 5 < 1?

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To solve -4x + 5 < 1, subtract 5 from both sides to get -4x < -4, then divide by -4 (remember to flip the inequality) to find x > 1.

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What is the difference between 'and' and 'or' in compound inequalities?

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In compound inequalities, 'and' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

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How do you solve the compound inequality x < -3 or x > 1?

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The solution includes all values of x that are either less than -3 or greater than 1, which can be expressed in interval notation as (-∞, -3) ∪ (1, ∞).

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What is absolute value?

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Absolute value is the distance of a number from zero on the number line, regardless of direction. It is denoted as |x|.