To solve this equation, we need to simplify it step by step to isolate the variable 'm' on one side of the equation.
Let's start by combining like terms. In this equation, we have '3m' on one side and '-3m' on the other side. Adding or subtracting the same variable on both sides of the equation cancels out that variable. Hence, '3m' and '-3m' cancel each other out, leaving us with:
54 - 3m/4 = -2
Next, let's isolate the term involving 'm'. We can do this by subtracting 54 from both sides of the equation:
54 - 3m/4 - 54 = -2 - 54
Simplifying further, we get:
-3m/4 = -56
To eliminate the denominator, we can multiply both sides of the equation by the reciprocal of (-4/3), which is (-3/4). This will cancel out the fraction on the left side:
(-3/4) * (-3m/4) = (-3/4) * (-56)
The left side simplifies to:
m = 42
Therefore, the value of 'm' that makes the equation true is 42.