how do you solve a problem like this
3X/4 = 7 + X/6
To solve the equation 3X/4 = 7 + X/6, you need to isolate the variable X on one side of the equation. Here's a step-by-step explanation of how to solve it:
1. Clear the fractions by multiplying every term in the equation by the least common denominator (LCD), which is 12 in this case. Multiply both sides of the equation by 12 to get rid of the fractions:
(12)(3X/4) = (12)(7) + (12)(X/6)
Simplifying, we have:
9X = 84 + 2X
Now we have a simplified equation without any fractions.
2. Combine like terms on both sides of the equation. In this case, we can combine the X terms on the right side of the equation:
9X - 2X = 84
Simplifying further, we get:
7X = 84
3. Now, isolate the variable X. To do this, divide both sides of the equation by the coefficient of X, which is 7:
(7X)/7 = 84/7
Simplifying, we have:
X = 12
So, the solution to the equation 3X/4 = 7 + X/6 is X = 12.