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When solving equations with fraction coefficients, it is easier if we eliminate the denominators first. This step helps to simplify the equation, making it look more familiar. Here’s how you can do it:

First, identify the denominators in the equation. In our example, the denominators are 6 and 3.
To eliminate them, find a common multiple of these denominators. In this case, 6 is a common multiple of both 6 and 3.
Multiply every term of the equation by this common multiple. For our example:

\[ \frac{4m + 2}{6} \times 6 = \frac{m}{3} \times 6 \]

The fractions will simplify, leaving you with an equation free of denominators:

\[ 4m + 2 = 2m \]

This simplification makes it much easier to work with and solve the equation. Eliminating denominators is a crucial first step in solving equations with fractions.

Once the denominators are gone, the next step is to isolate the variable. Isolating the variable means getting the variable by itself on one side of the equation. Here’s how to do it:

Take the simplified equation from the previous step. Our equation is now:

\[ 4m + 2 = 2m \]

We need to isolate m. To do this, we can subtract 2m from both sides. This step ensures that m is on its own on one side of the equation:

\[ 4m + 2 - 2m = 2m - 2m \]

Now this simplifies to:

\[ 2m + 2 = 0 \]

We have successfully isolated the variable on one side of the equation. Isolating the variable is essential, as it makes the final step of solving for the variable straightforward.

Finally, after isolating the variable, it’s time to solve for it. This will give you the final value of the variable in your equation. Here’s how to proceed:

Take the equation where the variable is isolated. From our previous step, we have:

\[ 2m + 2 = 0 \]

To solve for m, we need to get rid of the constant term on the left side. Subtract 2 from both sides to do this:

\[ 2m + 2 - 2 = 0 - 2 \]

This simplifies to:

\[ 2m = -2 \]

Next, divide both sides by 2 to solve for m:

\[ m = \frac{-2}{2} \]

This simplifies to:

\[ m = -1 \]

So, the solution to the equation is \[ m = -1 \]. Solving for the variable is the last and ultimate step in finding the value of the variable in your equation.