Answer:
To find the root of the equation \(\frac{m-3}{4} = \frac{m+1}{3}\), you can follow these steps:
Step 1: Cross-multiply to get rid of the fractions:
\(3(m-3) = 4(m+1)\)
Step 2: Distribute the constants on both sides of the equation:
\(3m - 9 = 4m + 4\)
Step 3: Move the \(4m\) term to the left side of the equation by subtracting \(4m\) from both sides:
\(3m - 4m - 9 = 4\)
Step 4: Combine like terms on the left side:
\(-m - 9 = 4\)
Step 5: Add 9 to both sides to isolate the variable \(m\):
\(-m = 4 + 9\)
\(-m = 13\)
Step 6: To solve for \(m\), multiply both sides by -1 to isolate \(m\):
\(m = -13\)
So, the root of the equation \(\frac{m-3}{4} = \frac{m+1}{3}\) is \(m = -13\).
Explanation: