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Test: Inequalities and intervals

Dynamic tasks on linear and compound inequalities, intervals and integer solutions. Word problems check the meaning of “at least” and “at most”.

Question qty: 10
Duration in minutes: 15
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Sample questions

  • Solve the inequality: x + a > b.
  • How many integers satisfy a < x < b?
  • Which interval represents a < x ≤ b?
  • Solve the inequality: −ax < b.
  • Does x belong to the interval (a, b]?
  • Solve the inequality: ax ≤ b.
  • A ticket costs €kaina. A student has at most €biudzetas. What is the greatest number of tickets the student can buy?
  • Write “a student must score at least a points” as an inequality. Let x be the number of points.

Inequalities and intervals

An inequality is solved similarly to an equation, but multiplying or dividing by a negative number reverses the inequality sign. Its solution is often an interval rather than a single number.

Boundaries

The symbols ≤ and ≥ include the boundary, while < and > exclude it. “At least” means ≥ and “at most” means ≤. Both conditions of a compound inequality must hold.

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