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Solving Linear Equations
Preserve equality by performing the same inverse operation on both sides until the variable is isolated.
How it works
Preserve equality by performing the same inverse operation on both sides until the variable is isolated. Name the quantities before calculating, keep each transformation logically equivalent, and check the result against the original conditions.
Worked example
Solve 4x+7=31.
- Subtract 7 from both sides: 4x=24.
- Divide both sides by 4.
- Check 4(6)+7=31.
x=6.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Using a remembered formula without identifying what each symbol represents.
- Changing a value or condition during an intermediate step.
- Skipping the final substitution, estimate, or logical check.
Challenge
Solve 3(x−2)+5=20 and check your result.
Questions learners ask
What is the key idea in solving linear equations?
Preserve equality by performing the same inverse operation on both sides until the variable is isolated.
How should I check an answer?
Substitute it into the original conditions, check units and signs, and decide whether its size is reasonable.