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?
- A mathematical statement comparing two expressions using <, >, <=, or >=
- Solve: x + 3 > 7
- x > 4
- Solve: 2x < 10
- x < 5
- Solve: -3x > 9
- x < -3 (the inequality flips)
- What must you do when multiplying or dividing both sides of an inequality by a negative number?
- Flip (reverse) the inequality symbol
- How is the solution to an inequality typically graphed on a number line?
- 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?
- The boundary value is not included (strict inequality)
- What does a closed (filled) circle mean on an inequality's number line graph?
- The boundary value is included
- What is a compound inequality?
- An inequality combining two conditions, often joined by 'and' or 'or'
- Solve the compound inequality: -2 < x < 5
- All x values between -2 and 5
- What does 'and' mean in a compound inequality, in terms of the solution set?
- The intersection of both conditions must be true
- What does 'or' mean in a compound inequality, in terms of the solution set?
- Either condition being true is sufficient
- What is an absolute value inequality, such as |x| < 3?
- An inequality involving absolute value, often producing a compound inequality solution
- Solve: |x| < 3
- -3 < x < 3
- Solve: |x| > 5
- x < -5 or x > 5
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