Solving equations with balance
Undo operations while keeping both sides of an equation equal.
Before you begin
- Signed-number arithmetic
- Order of operations
Keep the equality balanced
An equation asserts that two expressions have the same value. Adding, subtracting or multiplying both sides by the same number preserves equality; dividing is safe only when the divisor is nonzero. To isolate an unknown, reverse the operations around it. Write an operation on both sides rather than treating a symbol as magically changing sign when it crosses the equals sign.
Verify a solution by substitution
Solving and checking are different steps. After isolating the unknown, substitute the proposed value into the original equation. Evaluate each side using the original brackets and signs. If both values agree, the solution passes the check. This is especially useful when a negative coefficient or a bracket makes a sign error easy.
Worked example
Solve 3x + 5 = 26.
Show the worked solution
- Subtract 5 from both sides: 3x = 21.
- Divide both sides by 3: x = 7.
- Substitute into the original equation: 3 × 7 + 5 = 26.
x = 7.
Try it yourself
What is the solution of 4y − 3 = 17?
Common mistakes
- If you expand a bracket, multiply every term inside it.
What can you explain now?
Solve 2(x + 4) = 18 and check your answer.
Compare with the explanation
x = 5.
Divide both sides by 2 to get x + 4 = 9, then subtract 4. Checking gives 2(5 + 4) = 18.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗