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Linear Inequalities quiz

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  • What do square brackets in interval notation indicate about the endpoints?
    Square brackets indicate that the endpoint is included in the solution set.
  • How are open intervals represented in interval notation?
    Open intervals are represented with parentheses, meaning the endpoints are not included.
  • When graphing an interval, what does a closed circle on the number line represent?
    A closed circle represents that the endpoint is included in the solution set.
  • What must you do to the inequality symbol when multiplying or dividing both sides by a negative number?
    You must flip the direction of the inequality symbol.
  • How is infinity always represented in interval notation?
    Infinity is always enclosed in parentheses because it is not a specific, reachable value.
  • What is the first step when solving a linear inequality with fractions?
    Multiply both sides by the least common denominator to eliminate the fractions.
  • How do you express the solution to x is greater than or equal to 3 in interval notation?
    The solution is written as [3, ∞).
  • What is the interval notation for all x less than 5 but greater than 0?
    The interval notation is (0, 5).
  • If an inequality solution is x ≤ 2, how is this graphed on a number line?
    It is graphed with a closed circle at 2 and shading to the left.
  • What does a half-open interval look like in interval notation?
    A half-open interval uses a square bracket on one end and a parenthesis on the other, such as [0, 5).
  • What is the solution to -2x ≤ 6 after solving for x?
    The solution is x ≥ -3, after dividing by -2 and flipping the inequality.
  • Why do we use interval notation instead of set notation for inequalities?
    Interval notation is more compact and is specifically required for expressing solutions to inequalities.
  • How do you solve a linear inequality with variables on both sides?
    Move all variables to one side and constants to the other, then solve for the variable.
  • What does an open circle on a number line indicate when graphing an inequality?
    An open circle indicates that the endpoint is not included in the solution set.
  • How do you write the solution to x > -1 in interval notation?
    The solution is (-1, ∞).