Final answer:
To solve the inequality 1/4(5/12x-3/4)>x+1/12, simplify both sides of the equation, combine like terms. Therefore, the solution for x is x < -5/43.
Step-by-step explanation:
To solve the inequality 1/4(5/12x-3/4)>x+1/12, you can begin by simplifying both sides of the equation.
Start by distributing 1/4 to the terms inside the parentheses:
1/4 * 5/12x - 1/4 * 3/4 > x + 1/12
5/48x - 3/16 > x + 1/12
Next, combine like terms by subtracting x from both sides of the equation:
5/48x - x > 3/16 + 1/12
-43/48x > 5/48
Finally, divide both sides of the equation by -43/48 (remember to change the inequality sign when dividing by a negative number):
x < 5/48 / (-43/48)
x < -5/43
Therefore, the solution for x is x < -5/43.