Final answer:
The solution to the equation 2/3x + 6 = 1/2x + 1/4x is found by combining like terms and using common denominators. After simplifying, it is determined that x = 72.
Step-by-step explanation:
To solve the equation 2/3x + 6 = 1/2x + 1/4x, we first need to combine like terms. The terms 1/2x and 1/4x on the right side of the equation are like terms because they both contain the variable 'x'. To combine them, we convert them to a common denominator.
Putting 1/2 and 1/4 to a common denominator gives us 2/4 + 1/4, which equals 3/4. So, the equation becomes 2/3x + 6 = 3/4x. Next, to isolate the x terms on one side of the equation, we subtract 2/3x from both sides, which gives:
6 = 3/4x - 2/3x
Using common denominator for 3/4 and 2/3 gives us 9/12x - 8/12x, which simplifies to 1/12x. So now we have:
6 = 1/12x
Multiply both sides by 12 to solve for x:
72 = x
Therefore, the solution to the equation 2/3x + 6 = 1/2x + 1/4x is x = 72.