Chapter Summary

Solving linear equations

• Isolate the unknown by performing the same operation on both sides (balancing principle).
• For fractional coefficients: multiply both sides by the LCM of denominators to clear fractions.
• For fractional equations (unknown in denominator): multiply by the denominator expression, or cross-multiply.
• Always check by substituting your answer back into the original equation.

Word problems

• Define the variable, express the other quantities, form the equation, solve, then check in context.
• Translate English phrases carefully: "5 more than $3n$" $= 3n + 5$.