Solve the Linear Equation: Simplifying 7m + 3m - 40m = 0

To solve this problem, we'll proceed with the following steps:

• Step 1: Combine like terms of the given equation.
• Step 2: Solve for the variable $m$.

Now, let's work through these steps:

Step 1: Combine like terms:
We start with the equation $7m + 3m - 40m = 0$.
Combining these like terms entails adding or subtracting the coefficients of $m$:

$(7 + 3 - 40)m = 0$
Calculate the sum and difference of these coefficients:
$(10 - 40)m = 0$

This simplifies to:
$-30m = 0$

Step 2: Solve for $m$:
To isolate $m$, divide both sides by $-30$:
$m = \frac{0}{-30}$

Calculate the right-hand side:

$m = 0$

Therefore, the solution to the problem is $m = 0$. This corresponds to choice 3 from the provided answer options.