The inequality is .

Solve the inequality.

Step 1:

Since the radicand of a square root must be greaterthan or equal to zero, first solve and to identity the values of for which the left side of the inequality is define.

Case (i):

                               (First radicand greater than or equals to zero)

                   (Subtract from each side)

                                 (Apply additive inverse property: )

Case (ii):

                               (Second radicand greater than or equals to zero)

                    (Subtract from each side)

                                  (Apply additive inverse property: )

Step 2:

            (Original inequality)

   (Subtract from each side)

          (Apply additive inverse property: )

     (Take square on each side)

(Cancel square and root terms)

                   (Cancel common terms)

   (Subtract from each side)

                  (Apply additive inverse property: )

                        (Multiply negative sign each side and flip the symbol)

              (Take square each side)

                     (Cancel square and root terms)

                (Divide each side by )

                           (Cancel common terms)

                (Subtract from each side)

                              (Apply additive inverse property: )

                             (Simplify)

Step 3:

It appears that .

Check:

Use three test values and make a table:

Since is not a real number,the inequality is not satisfied.	Since is not a real number,the inequality is not satisfied.	Since ,the inequality is satisfied.

Thus, only values in the interval satisfy the inequality.

Graph:

The number line inequality is

The inequality solution set is .