Expressions and Equations
What this domain tests
Expressions and Equations tests simplifying linear expressions, solving multi-step equations and inequalities, and translating word problems into equations. Expect the distributive property, combining like terms, rational coefficients, and interpreting solutions.
Core rules
- Only like terms combine: 3x + 5x = 8x, but 3x + 5 stays 3x + 5.
- Distributive property: a(b + c) = ab + ac. Multiply every term inside the parentheses.
- Solve by undoing operations in reverse order; whatever you do to one side, do to the other.
- Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.
- Check a solution by substituting it into the original equation, not the simplified one.
Worked example
Solve 3(2x − 5) + 4 = 2x + 9. Distribute: 6x − 15 + 4 = 2x + 9. Combine: 6x − 11 = 2x + 9. Subtract 2x: 4x − 11 = 9. Add 11: 4x = 20. Divide by 4: x = 5. Check: left side 3(10 − 5) + 4 = 19; right side 10 + 9 = 19.
Inequality: −2x + 7 > 1. Subtract 7: −2x > −6. Divide by −2 and flip: x < 3. Test x = 0: 7 > 1 is true.
Traps that cost marks
- Distributing to the first term only: 3(2x − 5) becomes 6x − 5.
- Forgetting to flip the inequality sign after dividing by a negative.
- Combining 4x and 3 into 7x.
- Losing a negative sign when moving a term across the equals sign.
- Accepting an answer without checking, especially when the equation contains fractions.