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Linear Inequalities in One Variable quiz

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  • What is a linear inequality and how does it differ from a linear equation?
    A linear inequality is like a linear equation but uses an inequality symbol (>, <, ≥, ≤) instead of an equal sign. Its solutions are ranges of values rather than a single value.
  • How do you represent the solution to x > 3 in set builder notation?
    You write it as {x | x > 3}, which reads as 'the set of x such that x is greater than 3.'
  • What does a parenthesis on a number line indicate when graphing inequalities?
    A parenthesis indicates that the endpoint is not included in the solution set.
  • How do you write the solution to x ≥ 3 in interval notation?
    It is written as [3, ∞), using a square bracket to include 3 and a parenthesis for infinity.
  • What must you do to the inequality symbol when you multiply or divide both sides of an inequality by a negative number?
    You must flip the direction of the inequality symbol.
  • How do you solve the inequality x - 3 > 11?
    Add 3 to both sides to get x > 14.
  • What is the interval notation for x < 3?
    It is (-∞, 3), using parentheses to show that neither endpoint is included.
  • How do you represent x ≤ 3 on a number line?
    Draw an arrow to the left from 3 and use a square bracket or closed circle at 3 to show it is included.
  • What is a three-part (compound) inequality?
    It is an inequality where the variable is between two inequality symbols, such as -14 ≤ 2x - 10 < 2.
  • When solving a three-part inequality, what must you do to all three sides?
    You must perform the same operation on all three sides to maintain the inequality.
  • How do you write the solution to -2 ≤ x < 6 in interval notation?
    It is written as [-2, 6), with a bracket at -2 and a parenthesis at 6.
  • What does a square bracket mean in interval notation?
    A square bracket means the endpoint is included in the solution set.
  • If you solve -7x ≥ 21, what is the solution for x?
    Divide both sides by -7 and flip the inequality to get x ≤ -3.
  • What is the purpose of set builder notation in inequalities?
    Set builder notation describes the set of all values that satisfy the inequality.
  • How do you graph x > 3 on a number line?
    Draw an arrow to the right from 3 and use a parenthesis or open circle at 3 to show it is not included.