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11-53.

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.

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    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.

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    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.

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    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).