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US High School Compound Inequalities — practice questions

Explore 5 free Compound Inequalities questions in US High School Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Compound Inequalities questions and exercises with answers

Showing questions 1–5 of 5.

What makes an inequality a compound inequality?Read the answer and worked solution →For a compound inequality joined by and, which numbers form the solution?Read the answer and worked solution →Solve 2x + 1 greater than -3 and 3x - 4 less than or equal to 5, in interval notation.Read the answer and worked solution →Which symbol writes the solution of a compound inequality joined by or?Read the answer and worked solution →Sort the and and or stepsRead the answer and worked solution →

Worked practice questions

What makes an inequality a compound inequality?

  1. Two of them with the same sign
  2. Two of them joined by and or or
  3. One with two variables in it
  4. One with a squared term in it
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Correct answer: B. Two of them joined by and or or

1. A compound inequality is built from two separate inequalities. 2. The two are joined by the word and or the word or. 3. That joining word decides how the two separate solutions are combined. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.6 Solve Compound Inequalities_

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For a compound inequality joined by and, which numbers form the solution?

  1. Those that satisfy either part
  2. Those that satisfy neither part
  3. Those that satisfy the first part
  4. Those that satisfy both parts
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Correct answer: D. Those that satisfy both parts

1. Solve each inequality on its own first. 2. Graph both solutions and look for where the shading overlaps. 3. Only numbers that make both statements true survive that overlap. 4. Numbers satisfying just one part belong to an or problem, not an and problem. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.6 Solve Compound Inequalities_

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Solve 2x + 1 greater than -3 and 3x - 4 less than or equal to 5, in interval notation.

  1. The interval (-2, 3]
  2. The interval [-2, 3)
  3. The interval (-2, 3)
  4. The interval [-2, 3]
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Correct answer: A. The interval (-2, 3]

1. Take the first inequality on its own: 2x plus 1 greater than negative 3. 2. Subtract 1 to get 2x greater than negative 4, then divide by 2 to get x greater than negative 2. 3. Now take the second: 3x minus 4 less than or equal to 5. 4. Add 4 to get 3x less than or equal to 9, then divide by 3 to get x less than or equal to 3. 5. The joining word is and, so keep only the numbers satisfying both. 6. That is every number above negative 2 and up to 3 inclusive. 7. The strict sign at negative 2 gives a parenthesis, and the inclusive sign at 3 gives a bracket. 8. The interval [-2, 3) swaps the two endpoint marks around. 9. The interval (-2, 3) drops 3 even though the second inequality allows it. 10. The interval [-2, 3] adds negative 2 even though the first inequality excludes it. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.6 Solve Compound Inequalities_

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