Final answer:
To solve the equation 1/2*(x/3+1)=x/4-2, we distribute the 1/2, rearrange the equation to get x terms on one side, find a common denominator, and then isolate x to find that x equals 30.
Step-by-step explanation:
To solve for x in the equation 1/2*(x/3+1)=x/4-2, we need to perform several steps to isolate x and find its value. First, we can distribute the 1/2 through the parentheses on the left side of the equation:
1/2*(x/3) + 1/2*(1) = x/4 - 2
This simplifies to:
x/6 + 1/2 = x/4 - 2
Next, we want to get all the terms with x on one side and the constants on the other. We can do this by adding 2 to both sides and subtracting x/6 from both sides:
x/6 + 1/2 + 2 = x/4 - 2 + 2
x/6 + 5/2 = x/4
x/4 - x/6 = 5/2
To combine the fractions on the left side, we need a common denominator. Since 4 and 6 are both divisible by 12, we can write:
3x/12 - 2x/12 = 5/2
This simplifies to:
x/12 = 5/2
We multiply each side by 12 to solve for x:
x = 5/2 * 12
x = 30
So, the value of x that satisfies the equation is 30.