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Distribute the -(1)/(3) into the parenthesis.

Mathematics

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Answer

x>8x > 8

Step-by-step solution

4 steps

  1. Distribute the −13-\frac{1}{3} into the parenthesis.

    12x−13(x+4)>0\frac{1}{2}x - \frac{1}{3}(x+4) > 0 12x−13x−43>0\frac{1}{2}x - \frac{1}{3}x - \frac{4}{3} > 0

  2. Combine the xx terms by finding a common denominator.

    The common denominator for 2 and 3 is 6.

    36x−26x−43>0\frac{3}{6}x - \frac{2}{6}x - \frac{4}{3} > 0 16x−43>0\frac{1}{6}x - \frac{4}{3} > 0

  3. Add 43\frac{4}{3} to both sides of the inequality.

    16x>43\frac{1}{6}x > \frac{4}{3}

  4. Multiply both sides by 6 to solve for xx.

    x>43×6x > \frac{4}{3} \times 6 x>243x > \frac{24}{3} x>8x > 8
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