Pre-AlgebraPre-AlgebraMiddle school

One- and Two-Step Equations

Undo operations in reverse order to isolate the variable.

An equation is a balance: whatever you do to one side you must do to the other to keep it true. A one-step equation needs a single inverse operation to isolate the variable. Addition undoes subtraction, multiplication undoes division, and vice versa.

The goal is never to guess the answer but to produce a chain of equivalent equations ending in $x = \text{number}$ . Checking is quick: substitute the value back into the original equation and confirm both sides match.

Key terms

Inverse operations: Apply the same inverse operation to both sides so the equation stays balanced.
$3x + 5 = 20 \Rightarrow x = 5$

Key ideas

Identify the operation applied to the variable, then apply its inverse to both sides.
For $\frac{x}{a} = b$ multiply both sides by $a$ ; for $ax = b$ divide by $a$ .
Negative coefficients: divide by the negative number itself, as in $-4x = 20 \Rightarrow x = -5$ .
Always substitute back to check.

Worked example

Solve $\frac{x}{-3} = 7$ .

The variable is divided by $-3$ .
Multiply both sides by $-3$ : $x = 7 \times (-3)$ .
$x = -21$ .
Check: $\frac{-21}{-3} = 7$ . True.

Answer: $x = -21$

Common mistakes

Applying the inverse operation to one side only.
Dividing by $4$ instead of $-4$ and losing the sign.
Subtracting when the equation shows multiplication, as in turning $5x = 30$ into $x = 25$ .

Practice questions

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1.Solve $x - 9 = -4$ .
Show answer
$x = 5$
2.Solve $-6x = 42$ .
Show answer
$x = -7$
3.Solve $\frac{x}{5} = 2.4$ .
Show answer
$x = 12$

One- and Two-Step Equations

Key terms

Key ideas

Worked example

Common mistakes

Practice questions

Keep practising

Calculators

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