How To Solve Inequalities With Fractions

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Let’s take a few examples to show the steps to solve inequalities with fraction.

Question 1: - 5 x + 3 / 5 > 1 /2

Solution: -
i)             (5 x * 5 + 3 * 1) / 5 > 1 / 2
               (25 x + 3) / 5 > 1 / 2
               2* (25 x + 3) > 1 * 5
               2 * 25 x + 2 * 3 > 5
               50 x + 6 > 5
               50 x + 6 – 6 > 5 – 6
               50 x > - 1
               50 x / 50 > - 1 / 50
               x > - 1 / 50
Answer: - Therefore x > - 1 / 50



Question 2: - If (3 x / 2 - 2 x / 3) < (x / 5 – 1). Find the value of x.
 
Solution: -
              (3 x / 2 - 2 x / 3) < (x / 5 – 1)
              (3x * 3 – 2 x * 2) / 6 < (x * 1 – 1 * 5) / 5
              (9 x – 4 x) / 6 < (x – 5) / 5
              5 x / 6 < (x – 5) / 5
              5 * 5 x < 6 * (x – 5)
              25 x < 6 x – 30
              25 x – 6 x < 6 x – 30 – 6 x
              19 x < - 30
              19 x / 19 < -30 / 19
               X < - 30 / 19
 
Answer: - Therefore x < - 30 / 19.



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