x-5/6<x/2+3
x < 23/3
6x - 5 < 3x + 18
3x < 23
x < 23/3
To solve the inequality x - 5/6 < x/2 + 3, we need to isolate the variable x on one side of the inequality symbol.
First, let's simplify the expression on the right side:
x/2 + 3
To combine the terms, we need a common denominator. The common denominator here is 2:
(x/2) + (3*2/2)
= (x/2) + 6/2
= (x + 6)/2
Now, we can rewrite the inequality as:
x - 5/6 < (x + 6)/2
Next, let's clear the fractions by multiplying through all terms of the inequality by the denominators:
2(x - 5/6) < 6(x + 6)
Expanding the terms, we get:
2x - 5/3 < 6x + 36
Next, we can simplify the inequality further by moving all the terms with x to one side:
2x - 6x < 36 + 5/3
Simplifying the left side, we get:
-4x < 36 + 5/3
We can combine the terms on the right side:
-4x < (108 + 5)/3
-4x < 113/3
Finally, to isolate x, we divide both sides of the inequality by -4. Since we are dividing by a negative number, the inequality flips:
x > (113/3) / (-4)
x > -113/12
Therefore, the solution to the inequality is x > -113/12.