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Solve the inequalities and equations below. Represent your solutions for each inequality on a number line.

  1. Isolate the absolute value by subtracting from both sides.

    Change the inequality into an equation and solve for .

    Graph both values of on the number line, which divides the line into three regions.
    Substitute a value from each region into the original inequality.
    Whichever regions make the inequality true are the solutions.

    A number line is given. The graph starts with an open circle on negative 2 and is continuous until 2 where it is marked as an open circle.

  1. Change to an equation and solve for .

    Graph on a number line.
    Then check values from both regions to find the solution.

    Don't forget to represent your solution with a number line!

  1. Multiply both sides by as Fraction Buster to eliminate the fractions.

  1. Add x to both sides.

    Is this statement true? If so, then x can be any real number. If not, then there is no real solution.

  1. Subtract from both sides. Then divide by three.
    This will isolate the square root. Look inside to determine the solution.

  1. See the help for part (a).