Question

5x-12/4+x/12=x/3-1
The solution is

Answer 1

To solve the equation \(\frac{5x - 12}{4} + \frac{x}{12} = \frac{x}{3} - 1\), we first get rid of the fractions by finding a common denominator. In this case, the least common multiple of the denominators 4, 12, and 3 is 12.

We will multiply each term by 12:

\[
12 \left(\frac{5x - 12}{4}\right) + 12 \left(\frac{x}{12}\right) = 12 \left(\frac{x}{3}\right) - 12 \cdot 1
\]

This simplifies to:

\[
3(5x - 12) + x = 4x - 12
\]

Now distribute the \(3\) on the left side:

\[
15x - 36 + x = 4x - 12
\]

Combine like terms on the left side:

\[
16x - 36 = 4x - 12
\]

Next, isolate the \(x\) terms by subtracting \(4x\) from both sides:

\[
16x - 4x - 36 = -12
\]

This simplifies to:

\[
12x - 36 = -12
\]

Now, add \(36\) to both sides:

\[
12x = 24
\]

Finally, divide by \(12\):

\[
x = 2
\]

So the solution is:

\[
\boxed{2}
\]