Solve the equation 2x + 2 = 10.

Step-by-step solution

1. 1

   Undo the operations in reverse order. The left side was built by multiplying $x$ by $2$ and then adding $2$. To unwind it, reverse that order: remove the $+2$ first, and deal with the coefficient last. Subtract $2$ from both sides:

   $2x+2-2=10-2\qquad\Longrightarrow\qquad2x=8$

2. 2

   Divide by the coefficient.

   $\frac{2x}{2}=\frac{8}{2}\qquad\Longrightarrow\qquad x=4$

   Dividing before subtracting would also work but needs more care — it turns the equation into $x+1=5$, and forgetting to divide the $+2$ as well is a common slip.

3. 3

   Verify in the original equation. $2(4)+2=8+2=10$ ✓. The left side matches the right exactly.

4. 4

   Try the alternative route as a cross-check. Factoring the left side gives $2(x+1)=10$, so $x+1=5$ and $x=4$ ✓ — the same answer by a different path, which is good evidence the arithmetic is sound.

5. 5

   Note uniqueness. The equation is linear with a non-zero coefficient of $x$, so the line $y=2x+2$ meets the horizontal line $y=10$ exactly once. There is precisely one solution, and $x=4$ is it.