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Solving Linear Inequalities quiz

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  • What is the main difference between a linear equation and a linear inequality?
    A linear equation uses an equal sign and has a single solution, while a linear inequality uses an inequality symbol and has a range of solutions.
  • What are the four common inequality symbols used in linear inequalities?
    The four common symbols are greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤).
  • How is the solution to a linear inequality typically represented?
    The solution is a range of values, not just a single value, and can be shown using set builder notation, interval notation, or a number line.
  • What does set builder notation look like for the inequality x > 3?
    Set builder notation is written as {x | x > 3}, meaning the set of x such that x is greater than 3.
  • How do you indicate that a boundary value is not included in interval notation?
    You use parentheses, for example (3, ∞) means values greater than 3 but not including 3.
  • What notation is used to show that a boundary value is included in interval notation?
    Square brackets are used, for example [3, ∞) means values greater than or equal to 3.
  • How do you graphically represent the exclusion of a value on a number line?
    You use a parenthesis or an open circle at the boundary value to show it is not included.
  • What is the interval notation for x < 3?
    The interval notation is (-∞, 3), using parentheses to show neither boundary is included.
  • What is the interval notation for x ≤ 3?
    The interval notation is (-∞, 3], with a square bracket at 3 to show it is included.
  • What must you do to the inequality symbol when multiplying or dividing both sides by a negative number?
    You must flip the inequality symbol to maintain a true statement.
  • How do you solve the inequality x - 3 > 11?
    Add 3 to both sides to isolate x, resulting in x > 14.
  • What is the solution to the inequality -7x ≥ 21?
    Divide both sides by -7 and flip the inequality, giving x ≤ -3.
  • What is a three-part (compound) inequality?
    It is an inequality where the variable expression is between two inequality symbols, such as -14 ≤ 2x - 10 < 2.
  • When solving a three-part inequality, what must you do with each operation?
    You must perform the operation on all three sides of the inequality.
  • How is the solution to -2 ≤ x < 6 written in interval notation?
    It is written as [-2, 6), with a bracket at -2 and a parenthesis at 6.