Solve the equation 2x + 5 = 13.

Step-by-step solution

1. 1

   Isolate the term containing $x$ first. The constant $+5$ is the outermost operation, so it is removed before the coefficient. Subtract $5$ from both sides:

   $2x+5-5=13-5\quad\Longrightarrow\quad 2x=8$

2. 2

   Divide by the coefficient of $x$. The coefficient is $2$, so divide both sides by $2$:

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

3. 3

   Why the order matters. Dividing by $2$ first would give $x+\tfrac52=\tfrac{13}{2}$ — still correct, but now every number is a fraction. Clearing the constant first keeps the arithmetic in whole numbers.

4. 4

   Check by substitution. Put $x=4$ into the original left-hand side:

   $2(4)+5=8+5=13\qquad\checkmark$

   The two sides agree, so $x=4$ is the unique solution — a linear equation with a nonzero coefficient always has exactly one.