Algebra and Basic Equations
Algebra and Basic Equations
This domain covers simplifying algebraic expressions, expanding brackets, solving linear equations, substitution, and checking solutions. The exam expects clear inverse-operation steps rather than trial and error. Most marks are lost through sign slips and incomplete distribution rather than difficulty.
Core rules
- Collect like terms only when the variable and power match: 3x + 5x = 8x, but 3x + 5x² cannot be combined.
- Expand brackets with the distributive law: a(b+c) = ab + ac. Watch signs when the factor is negative.
- Solve linear equations by doing the same operation to both sides: remove brackets, collect variables on one side, collect constants on the other, then divide by the coefficient.
- Substitute by replacing the variable with brackets, then apply order of operations. Always check the solution in the original equation.
- For inequalities, the same balance method applies, but reverse the inequality sign when multiplying or dividing by a negative number.
Worked example
Solve 3(2x − 5) = 4x + 7. Expand: 6x − 15 = 4x + 7. Subtract 4x from both sides: 2x − 15 = 7. Add 15: 2x = 22. Divide by 2: x = 11. Check: left side 3(22 − 5) = 3(17) = 51; right side 4(11) + 7 = 51. Correct.
Traps
Forgetting to multiply the second term inside brackets; dropping a negative sign when expanding −(x − 4); dividing only one side; cancelling terms across a plus sign; and accepting an answer without substituting it back.