How do you solve and write the following in interval notation: x - 48 x &lt; - 8

Question

How do you solve and write the following in interval notation:       x    -          48      x        &amp;lt;    -    8

iskakanjulc · Accepted Answer

Step 1Put on a common denominator.            x      2        -    48    &amp;lt;    -    8    x              x      2        +    8    x    -    48    &amp;lt;    0  Solve as an equation:            x      2        +    8    x    -    48    =    0              (      x      +      12      )              (      x      -      4      )        =    0        x    =    -    12                or              4  Now select a test point, let it be       x    =    1        1    -          48      1              &amp;lt;      ?        -    8        1    -    48    &amp;lt;    -    8  Therefore, the solution is       x    ∈          (      -      12      ,      4      )       Note the circular brackets instead of the square brackets. This is because the points -12 and 4 are not included in the solution.

Cristopher Knox · Accepted Answer

Step 1We&#039;ll solve by a sign table (sign chart, sign analysis)Make one side 0.      x    -          48      x        +    8    &amp;lt;    0  The important point (the partition numbers) are -12, 0 and 4                              I          n          t          e          r          v          a          l          :                            (        −        ∞        ,                 −        12        )                    (        −        12        ,                 0        )                    (        0        ,                 4        )                    (        4        ,                 ∞        )                            ↓        Factors                 ↓                            x        +        12                    −                    +                    +                    +                            x        −        4                    −                    −                    +                    +                                                  (            x            +            12            )            (            x            −            4            )                    x                            −                    +                    −                    +            So the solution set is             (      -      ∞      ,      -      12      )        ∪          (      0      ,      4      )

How do you solve and write the following in interval notation: <mstyle displaystyle="true">

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