Algebra 1, Unit 5: Inequalities. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is an inequality?
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A mathematical statement comparing two expressions using <, >, <=, or >=- Solve: x + 3 > 7
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x > 4- Solve: 2x < 10
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x < 5- Solve: -3x > 9
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x < -3 (the inequality flips)- What must you do when multiplying or dividing both sides of an inequality by a negative number?
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Flip (reverse) the inequality symbol- How is the solution to an inequality typically graphed on a number line?
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As a ray, with an open or closed circle at the boundary point- What does an open circle mean on an inequality's number line graph?
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The boundary value is not included (strict inequality)- What does a closed (filled) circle mean on an inequality's number line graph?
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The boundary value is included- What is a compound inequality?
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An inequality combining two conditions, often joined by 'and' or 'or'- Solve the compound inequality: -2 < x < 5
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All x values between -2 and 5- What does 'and' mean in a compound inequality, in terms of the solution set?
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The intersection of both conditions must be true- What does 'or' mean in a compound inequality, in terms of the solution set?
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Either condition being true is sufficient- What is an absolute value inequality, such as |x| < 3?
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An inequality involving absolute value, often producing a compound inequality solution- Solve: |x| < 3
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-3 < x < 3- Solve: |x| > 5
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x < -5 or x > 5
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