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.
12x + 9 = 4x + 7
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.
\(\frac{\mathrm{8x} }{\mathrm{8}} =\frac{\mathrm{-2} }{\mathrm{8} }\)
\(x=\frac{\mathrm{-1} }{\mathrm{4} }\)