Treat the equation like a balance
An equation says that two expressions have the same value. To preserve its solutions, add or subtract the same quantity on both sides, or multiply or divide both sides by the same nonzero quantity.
Trace the operations applied to the variable, then undo them in reverse order. For an equation in the form ax + b = c with a ≠ 0, undo the added or subtracted constant first and then undo the multiplication by a; a differently structured equation can require a different first step.
Check, do not just stop
After you find a value, substitute it into the original equation. If both sides simplify to the same number, the value is a solution.
A check catches sign mistakes and skipped operations. It also turns the final line into evidence instead of a guess.
Remember these ideas
Key ideas
- Preserve the solutions by applying the same valid operation to both sides.
- Identify the operations applied to the variable and undo them in reverse order.
- Write one change per line so the reasoning stays visible.
- Substitute the result into the original equation to check it.
Make the reasoning visible
Worked example · 2x + 5 = 17
- 1
Subtract 5 from both sides: 2x + 5 − 5 = 17 − 5.
- 2
Simplify: 2x = 12.
- 3
Divide both sides by 2: x = 6.
- 4
Check: 2(6) + 5 = 17, so the solution works.
Try the next step
Solve and check
Solve 5x + 7 = 32, then substitute your answer into the original equation to check it.
Dividing every term by 5 first is valid. Why does subtracting 7 first keep the arithmetic easier to track?