Algebra
Solving linear equations
A linear equation states that two expressions are equal. Solving it means isolating the variable using operations that keep both sides balanced: add, subtract, multiply or divide the same quantity on each side.
Why it matters
Most later topics — systems, inequalities, quadratics, rearranging formulas in science — depend on fluent, accurate equation solving. Students who lose marks in Algebra 2 often lose them here, not in the new material.
Worked example
Solve 3(x − 4) + 5 = 2x + 7
- 1Expand the bracket. 3x − 12 + 5 = 2x + 7
- 2Collect like terms on the left. 3x − 7 = 2x + 7
- 3Subtract 2x from both sides. x − 7 = 7
- 4Add 7 to both sides. x = 14
Answer: x = 14
Common mistakes
- Distributing to the first term only: writing 3x − 4 instead of 3x − 12.
- Changing one side without changing the other.
- Dropping a negative sign when moving terms across the equals sign.
How to check your answer
- Substitute your answer back into the original equation — both sides must match.
- If the variable disappears, decide whether the result is always true (infinite solutions) or never true (no solution).
Related topics
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