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AP Intermediate 1st Year Linear Inequalities — practice questions

Explore 50 free Linear Inequalities questions in AP Intermediate 1st Year 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 1–30 of 50.

Two real numbers or two algebraic expressions related by <, >, ≤ or ≥ form:Read the answer and worked solution →Which of the following is a STRICT inequality?Read the answer and worked solution →Solve 30x < 200 where x is a natural number. The solution set is:Read the answer and worked solution →Solve 5x - 3 < 3x + 1 where x is an integer.Read the answer and worked solution →Add the same number 5 to both sides of -4 ≤ -2. The result is:Read the answer and worked solution →Divide BOTH sides of -6x ≥ 24 by -3. Result:Read the answer and worked solution →Identify the linear inequality in TWO variables.Read the answer and worked solution →Solve -3x + 5 > 2 over real numbers.Read the answer and worked solution →Identify a QUADRATIC inequality (not a linear inequality).Read the answer and worked solution →Solve 3 ≤ 2x - 1 ≤ 7 (a DOUBLE inequality) for real x.Read the answer and worked solution →In one variable, the inequality 2(x - 1) ≥ x + 5 solves to:Read the answer and worked solution →Solve the inequality (x - 3)/2 + 1 < 0 over real numbers.Read the answer and worked solution →In the inequality 3x + 5 ≤ 2x + 7, after using Rule 1 to move x-terms to one side:Read the answer and worked solution →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 →Tap every inequality symbolRead the answer and worked solution →True or false: inequalitiesRead the answer and worked solution →Both sides of 3 > 2 are multiplied by -1. Which statement results?Read the answer and worked solution →Which inequality says that x is at most 7?Read the answer and worked solution →ax + b ≥ 0 with a ≠ 0 is a linear inequality in how many variables?Read the answer and worked solution →ax² + bx + c > 0 with a ≠ 0 is what kind of inequality?Read the answer and worked solution →Which set lists the natural numbers x satisfying 3x < 12?Read the answer and worked solution →What is the largest natural number x with 30x < 200?Read the answer and worked solution →Dividing -5x ≤ -40 by -5 gives which inequality?Read the answer and worked solution →

Worked practice questions

Two real numbers or two algebraic expressions related by <, >, ≤ or ≥ form:

  1. An inequality
  2. A relation
  3. An equation
  4. A function
Show answer and solution

Correct answer: A. An inequality

An inequality is a statement relating two quantities by <, >, ≤ or ≥ (not the equality sign =). Equations use =, functions are mappings, relations are subsets of A × B.

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Which of the following is a STRICT inequality?

  1. x ≥ 3
  2. x = 3
  3. x ≤ 3
  4. x < 3
Show answer and solution

Correct answer: D. x < 3

Strict inequalities use < or > (without equality). Slack inequalities use ≤ or ≥. x = 3 is an equation. x < 3 strictly excludes 3.

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Solve 30x < 200 where x is a natural number. The solution set is:

  1. {0, 1, 2, 3, 4, 5, 6}
  2. {1, 2, 3, 4, 5, 6, 7}
  3. {1, 2, 3, 4, 5, 6}
  4. {... -1, 0, 1, 2, 3, 4, 5, 6}
Show answer and solution

Correct answer: C. {1, 2, 3, 4, 5, 6}

30x < 200 → x < 20/3 ≈ 6.67. Natural numbers start at 1 (As per your syllabus, convention here), so solution set = {1, 2, 3, 4, 5, 6}.

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More Mathematics topics

Sets and RelationsBinomial TheoremLimits and DerivativesSequences and SeriesStraight Lines and Conic SectionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsStatistics and Probability