5 - 2x/3 > 1/2 + x/4

To solve this inequality, we need to isolate the variable x on one side of the inequality sign.

First, let's simplify the inequality:

5 - 2x/3 > 1/2 + x/4
Multiply all terms by 12 to get rid of the fractions:
12(5) - 12(2x/3) > 12(1/2) + 12(x/4)
60 - 8x > 6 + 3x

Now, let's move all terms involving x to one side of the inequality sign:

60 - 8x - 3x > 6
60 - 11x > 6

Next, let's isolate x by moving all terms not involving x to the other side of the inequality sign:

-11x > 6 - 60
-11x > -54

Finally, divide by -11 to solve for x:

x < -54 / -11
x < 54/11
x < 4.909

Therefore, the solution to the inequality is x < 4.909.

5 - 2x/3 > 1/2x/4

First, let's simplify the inequality:

5 - 2x/3 > 1/2 - 2x/4
5 - 2x/3 > x/4

Now, let's multiply both sides by the least common multiple of the denominators, which is 12:

12(5 - 2x/3) > 12(x/4)
60 - 24x > 3x

Now, let's simplify further:

60 > 24x + 3x
60 > 27x

Finally, let's isolate x by dividing both sides by 27:

60/27 > x
2.22... > x

Therefore, the solution to the inequality is x < 2.22...