A reliable method
Collect variable terms and constants separately. For a system, use substitution or elimination and verify the resulting ordered pair in both original equations.
The common trap
Moving a term is shorthand for applying an operation to both sides. That shorthand can hide a sign error if you do not know which operation it represents.
Check and transfer
Represent the final answer in the form requested. A boundary value, a solution interval and one coordinate of a system are related but are not interchangeable outputs.
Worked comparison: identify the structure
Solve (2x−3)/4=5 by clearing the denominator: 2x−3=20, then x=23/2. Adding three before multiplying only the right side by four would change the original equation. Substitute back to check that the original fraction equals five.
Transfer and explain
For −2x+7<1, subtract seven to get −2x<−6, then divide to get x>3. The boundary number and the direction are separate parts of the solution; test x=4 in the original inequality.
Solve (2x − 2)/3 = 5. What is x?
- Multiply both sides by 3.
- Add the subtracted constant before dividing by the coefficient of x.
- The requested value is 17/2. Substitute or reverse the operation to check this result.
Compare the other answer choices
Stop before dividing the x coefficient two.
Omit multiplication of the right side by three.
Divide by three again after clearing the fraction.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
CLEP College Algebra exam overviewSiyavula Grade 10 foundation reference