Solving Linear Equations — One Step.

An equation says two things are equal. The variable (usually $x$, but any letter) is the unknown we want to find. $x + 5 \;=\; 12$

To solve is to find the value of $x$ that makes the equation true.

The golden rule

Whatever you do to one side, do to the other. This keeps the equation balanced — like a scale. Add to one side, you must add the same to the other.

One-step equations

The variable already has just one operation done to it. Undo that operation by doing the opposite to both sides.

Plus → minus

$x + 5 \;=\; 12$ Subtract $5$ from both sides: $x + 5 - 5 \;=\; 12 - 5 \;\Rightarrow\; x = 7$

Minus → plus

$x - 4 \;=\; 9$ Add $4$ to both sides: $x = 13$

Times → divide

$3x \;=\; 21$ Divide both sides by $3$: $x = 7$

Divide → times

$\frac{x}{4} \;=\; 5$ Multiply both sides by $4$: $x = 20$

Always check by substituting back

If you got $x = 7$ for $x + 5 = 12$, plug it back in: $7 + 5 = 12$ ✓. This catches arithmetic errors before they become bigger problems.