How to solve linear equations and check the answer
Keep both sides equal, handle brackets carefully and substitute your result back into the original equation.
Quick answer
Use the same operation on both sides to isolate the unknown, simplify carefully and check the result in the original equation. A correct substitution is a stronger check than rereading the final number.
An equation says two expressions have equal values. Solving it means finding the value that keeps that statement true, not just moving symbols until x is on its own.
An equation with brackets
Solve 3(x − 2) = 21. Divide both sides by 3: x − 2 = 7. Add 2 to both sides: x = 9. Check in the original: 3(9 − 2) = 3 × 7 = 21.
You could also expand the brackets to 3x − 6 = 21 and get the same answer. Choose a valid route that keeps the arithmetic simple.
Unknowns on both sides
For 4x − 5 = 2x + 11, subtract 2x from both sides to get 2x − 5 = 11. Add 5, giving 2x = 16, then divide by 2: x = 8. Both original sides equal 27.
Watch the sign
If −2x = 10, divide by −2, not by 2. The solution is x = −5, and (−2) × (−5) = 10. A lost negative sign changes the answer even if the remaining arithmetic is correct.
How to review an error
Write each operation beside your working and check the first line where equality no longer holds. Try the public mathematics examples and record the error pattern in notes.
Sources and further reading
Reference material supports the explanations.
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