A reliable method
Undo addition or subtraction on both sides, then undo multiplication or division. For variables on both sides, collect variable terms together before isolating the unknown.
The common trap
A fee plus an hourly rate is not a single rate. Subtract the fixed fee from the total before dividing by the hourly charge.
Check and transfer
Put the candidate answer back into the original situation. Check both the equality and whether the quantity makes sense: hours, items and money may have different restrictions.
Worked comparison: why the alternative fails
A bill of $34 has a $10 fixed fee and costs $6 per hour. Solve 10 + 6h = 34 to get h = 4. Dividing 34 by 6 leaves the fixed charge inside the labor cost and cannot describe the billed hours.
Transfer and explain
Solve 5x + 2 = 3x + 12: subtract 3x and then 2 to get 2x = 10, so x = 5. Substitution gives 27 on both sides.
A repair bill is $46, including an $18 visit fee and $7 per hour. How many hours were billed?
- Subtract the fixed visit fee from the total.
- Divide the remaining labor charge by dollars per hour.
- The requested value is 4. Check its units and meaning against the original question.
Compare the other answer choices
Report the labor cost instead of the hours.
Divide the entire bill by the hourly charge, including the fixed fee.
Add the visit fee when it should be removed.
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.
GED Mathematical Reasoning overviewSiyavula Grade 10 mathematics foundation reference