The student's equation is an incorrect equation because it is incorrectly solved.
One way we know this is that adding 6 to both sides of the equation should result in 18 on the right-hand side, not 12.
Let's go through the correct step-by-step solution to the equation \(2x - 6 = 12\):
1. Start with the given equation:
[tex]\[
2x - 6 = 12
\][/tex]
2. Add 6 to both sides of the equation:
[tex]\[
2x - 6 + 6 = 12 + 6
\][/tex]
3. Simplify both sides:
[tex]\[
2x = 18
\][/tex]
4. Divide both sides by 2 to solve for \(x\):
[tex]\[
\frac{2x}{2} = \frac{18}{2}
\][/tex]
5. Simplify the expression:
[tex]\[
x = 9
\][/tex]
This shows that the correct solution to the equation [tex]\(2x - 6 = 12\)[/tex] is [tex]\(x = 9\)[/tex].
