Solving one-step equations
Model a situation, undo one operation and verify a rational-number solution.
Before you begin
- Inverse operations
- Fraction and decimal arithmetic
Keep both sides balanced
An equation remains true when you perform the same valid operation on both sides. To solve x + p = q, subtract p from each side. To solve px = q with p nonzero, divide both sides by p. The operation is justified by equality, not by a rule that symbols change sign when moved. Write each new balanced equation clearly.
Define the unknown before choosing an operation
Read the story and define what the variable measures. A starting amount plus an unknown amount suggests addition; a fixed number of identical groups suggests multiplication. After solving, substitute into the original statement and check the unit and context. A numerical result can satisfy the algebra but still be unreasonable if a count must be a whole number.
Worked example
Three identical packets have total mass 7.5 kg. Find the mass m of one packet.
Show the worked solution
- The model is 3m = 7.5 because there are three equal masses.
- Divide both sides by 3: m = 2.5.
- Check: 3 × 2.5 kg = 7.5 kg, so the result fits the total.
m = 2.5 kg.
Try it yourself
Solve x + 3/4 = 2.
Common mistakes
- Apply the same operation to both sides.
- Check the answer in the original equation, with units.
What can you explain now?
A ribbon plus 1.8 m measures 5 m. Write and solve an equation for its original length r.
Compare with the explanation
r + 1.8 = 5; r = 3.2 m.
Subtract 1.8 from both sides. Checking gives 3.2 + 1.8 = 5 metres.
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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 ↗