Solve the equation:
\(12x + 9 = 4x + 7\)

We need to isolate all terms containing \(x\) on one side of the equation. We can eliminate \(4x\) from the right-hand side of \(12x + 9 = 4x + 7\) by subtracting \(4x\) from both sides of the equation.
Subtract \(4x\) from both sides.
\(12x + 9 -4x = 4x + 7 - 4x\)
\(8x + 9 = 7\)
Next, eliminate 9 from the left-hand side of the last equation by subtracting 9 from both sides of the equation.
\(8x + 9 - 9= 7 - 9\)
\(8x = -2\)
Note how we have isolated all terms containing \(x\) on one side of the equation. Finally, to “undo” multiplying by 8, divide both sides of the equation by 8 and reduce to the lowest terms.
\(\frac{\mathrm{8x} }{\mathrm{8}} =\frac{\mathrm{-2} }{\mathrm{8} }\)
\(x=\frac{\mathrm{-1}}{\mathrm{4} }\)