Algebra
Single-variable equations
Solving equations
20 practice questions
2 video lessons
Theory + worked examples
Theory
An equation states two expressions are equal. To solve it, isolate the variable by undoing operations:
- Use the inverse operation (add/subtract, multiply/divide).
- Do the same to both sides to keep it balanced.
- Check by substituting the answer back.
An equation is a balance: what you do to one side you must do to the other.
An equation balances both sides.
Steps to solve.
Inverse operations:
\[+\ \leftrightarrow\ -,\qquad \times\ \leftrightarrow\ \div\]
Undo in reverse order of operations.
How to solve
- Identify the operation on the variable.
- Apply its inverse to both sides.
- Simplify to isolate the variable.
- Check the solution.
Example 1 — Subtract to undo
Solve \(x+5=12\).
Solution
Subtract \(5\) from both sides.
| \(x+5-5\) | \(=\) | \(12-5\) |
| \(x\) | \(=\) | \(7\) |
Example 2 — Divide to undo
Solve \(3x=15\).
Solution
Divide both sides by \(3\).
| \(\dfrac{3x}{3}\) | \(=\) | \(\dfrac{15}{3}\) |
| \(x\) | \(=\) | \(5\) |
Example 3 — Multiply to undo
Solve \(\dfrac{x}{4}=3\).
Solution
Multiply both sides by \(4\).
| \(x\) | \(=\) | \(3\times4\) |
| \(=\) | \(12\) |
Example 4 — Check the solution
Verify \(x=7\) solves \(x+5=12\).
Solution
Substitute back.
| \(7+5\) | \(=\) | \(12\ \checkmark\) |
Common pitfalls
Do the same to both sides — always.
Use the inverse operation, not the same one.
Check your answer by substituting back.
Frequently asked questions
What does it mean to solve an equation?
Find the value of the variable that makes it true.
How do you solve \(x+5=12\)?
Subtract \(5\) from both sides: \(x=7\).
Why do the same to both sides?
To keep the equation balanced and true.
How do you check a solution?
Substitute it back and confirm both sides are equal.
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