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US High School Linear Inequalities — practice questions

Explore 8 free Linear 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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Linear Inequalities questions and exercises with answers

Showing questions 1–8 of 8.

How is the inequality x greater than 3 written in interval notation?Read the answer and worked solution →Which inequality symbol matches the phrase is at least?Read the answer and worked solution →Solve the inequality negative 5x greater than 20.Read the answer and worked solution →What happens to an inequality sign when the same number is added to both sides?Read the answer and worked solution →Solve 3(x - 2) less than or equal to 5x + 4 and write the answer in interval notation.Read the answer and worked solution →How is the inequality x less than or equal to 1 written in interval notation?Read the answer and worked solution →Knock out the false inequality claimsRead the answer and worked solution →Cluster inequalities by what they shadeRead the answer and worked solution →

Worked practice questions

How is the inequality x greater than 3 written in interval notation?

  1. The interval (3, infinity)
  2. The interval [3, infinity)
  3. The interval (infinity, 3)
  4. The interval (0, 3)
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Correct answer: A. The interval (3, infinity)

1. Every number to the right of 3 satisfies the inequality, but 3 itself does not. 2. An excluded endpoint is written with a parenthesis rather than a bracket. 3. There is no upper end, so infinity closes the interval, giving (3, infinity). _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.5 Solve Linear Inequalities_

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Which inequality symbol matches the phrase is at least?

  1. Strictly greater than
  2. Strictly less than
  3. Greater than or equal to
  4. Less than or equal to
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Correct answer: C. Greater than or equal to

1. Everyday phrases have to be matched to inequality symbols before solving. 2. Is at least allows the stated value itself as well as everything above it. 3. That combination is greater than or equal to. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.5 Solve Linear Inequalities_

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Solve the inequality negative 5x greater than 20.

  1. x is more than -4
  2. x is less than -4
  3. x is less than 4
  4. x is more than 4
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Correct answer: B. x is less than -4

1. Divide both sides by negative 5 to get x on its own. 2. Because the divisor is negative, the inequality sign reverses. 3. The right side becomes 20 divided by negative 5, which is negative 4. 4. So the solution is x less than negative 4. 5. Keeping the sign pointing the same way gives x more than negative 4, which fails a test value. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.5 Solve Linear Inequalities_

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