Solving One-Step Equations
See every one-step equation as the same job: identify the single operation attached to x, undo it with its inverse, and mirror that operation on both sides.
What operation is hiding x, and what operation undoes it?
A one-step equation has exactly one operation between x and isolation. The equal sign is a promise that both sides have the same value, so any change must be mirrored.
Apply the inverse operation to both sides. The operation on x cancels; equality survives.
Four surface forms, one pattern.
The arithmetic changes, but the solving logic does not. Find the attached operation and use its inverse.
Undo the operation, on both sides.
Which operation isolates x?
Every option below is applied to both sides. The question is which one actually undoes the operation attached to x.
Solve first. Substitution checks the value you derived; it does not discover the value for you.
“Move it across and change the sign” is shorthand, not the rule.
In x + 6 = 14, the +6 does not teleport across the equal sign. We subtract 6 from both sides. The left-side +6 and −6 cancel, leaving x = 8.
The equation may look different; its solution must stay the same.
Balanced operations create equivalent equations. A legal but unhelpful move can preserve the solution while making x harder to isolate.
Subtract 6 from both sides.
Add 6 to both sides.