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Distribute the (1)/(2) on the left side of the inequality.

Mathematics

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Answer

x≥−35x \ge -\frac{3}{5}

Step-by-step solution

5 steps

  1. Distribute the 12\frac{1}{2} on the left side of the inequality.

    x+12≥13x+110x + \frac{1}{2} \ge \frac{1}{3}x + \frac{1}{10}

  2. To eliminate the fractions, multiply every term by the least common multiple (LCM) of the denominators (2, 3, and 10).

    The LCM of 2, 3, and 10 is 30.

    30(x)+30(12)≥30(13x)+30(110)30(x) + 30\left(\frac{1}{2}\right) \ge 30\left(\frac{1}{3}x\right) + 30\left(\frac{1}{10}\right) 30x+15≥10x+330x + 15 \ge 10x + 3

  3. Collect all terms involving xx on one side and constant terms on the other side.

    Subtract 10x10x from both sides:

    30x−10x+15≥330x - 10x + 15 \ge 3 20x+15≥320x + 15 \ge 3

    Subtract 15 from both sides:

    20x≥3−1520x \ge 3 - 15 20x≥−1220x \ge -12

  4. Divide by 20 to solve for xx.

    x≥−1220x \ge \frac{-12}{20}

  5. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4.

    x≥−35x \ge -\frac{3}{5}
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