Question

PLEASE HELP!!!!!!!!!!!!!!!!! Solve. −1/2x + 1/3 > 3/5

Answer 1

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.

Answer:
x < -8/15

Hope this helps!