To solve this inequality, you must first isolate the term that includes the variable, which is -1/2x. This can be done by first subtracting 1/3 from both sides.
Before you can subtract 1/3 from 3/5, however, you must first convert the fractions to have common denominators. A common denominator for 1/3 and 3/5 is 15. This is the LCM, least common multiple, of 3 and 5, making it the lowest possible common denominator. Using this common denominator, 1/3 changes to 5/15 and 3/5 changes to 9/15.
Now we can subtract these equivalent fraction for 1/3, which is 5/15, from the fraction equivalent to 3/5, which is 9/15. 9/15 - 5/15 = 4/15 This fraction can't be simplified any further so this step is done.
Now the inequality is -1/2x > 4/15. The next step is to isolate x by dividing both sides by -1/2. An important note to remember when doing this step is that whenever dividing by a negative in inequalities, you must flip the inequality symbol. In this case, that means dividing both sides by -1/2 and changing the greater than sign (>) to a less than sign (<).
-1/2x ÷ -1/2 = x
4/15 ÷ -1/2 When dividing fractions, find the reciprocal of the second fraction then multiply. The reciprocal of -1/2 is -2/1, or -2 when simplified. 4/15 • -2 = -8/15
This means x < -8/15. This has x isolated and the inequality simplified as far as possible. That means this is the answer.
