To solve the equation \(\frac{3x + 12}{3} - 1 = \frac{4x + 16}{2}\), we start by simplifying both sides.
Step 1: Simplify the left-hand side: \[ \frac{3x + 12}{3} - 1 = x + 4 - 1 = x + 3 \]
Step 2: Simplify the right-hand side: \[ \frac{4x + 16}{2} = 2x + 8 \]
Now our equation looks like this: \[ x + 3 = 2x + 8 \]
Step 3: Rearranging the equation: Next, we'll isolate \(x\) by moving all the \(x\) terms to one side and the constants to the other side. \[ x - 2x = 8 - 3 \] \[ -x = 5 \] Multiplying both sides by -1 gives us: \[ x = -5 \]
Conclusion: The solution to the equation is \(x = -5\).
Since we found exactly one value of \(x\), the linear equation has one solution.