Mathematics · Grades 6–9
Equations, expressions and equivalent steps
Preserve equality and check a solution in the original equation.
Learn the idea
Expression or equation
An expression represents a value; an equation asserts equality between two expressions.
Balance
Applying the same valid operation to both sides preserves an equation. Division by zero is never valid.
Distribute
a(b + c) = ab + ac. The multiplier acts on every term inside the brackets.
Check
Substitute a proposed solution into the original equation, not just a rearranged line.
Worked examples
Which item is an equation?
The equals sign asserts that two expressions have equal values.
3x + 2 = 11
Solve 3x + 2 = 11 for x.
Subtract 2 to obtain 3x = 9, then divide by 3.
3
Check your understanding
Solve 4(x − 2) = 20 for x.
Which expression equals 5(a + 3)?
- 5a + 3
- 5a + 15
- a + 15
Evaluate 2p² − 3 when p = −2.
Answers and marking notes
Answers and marking notes
- 7
Divide by 4 to get x − 2 = 5, then add 2.
- 5a + 15
The 5 multiplies both a and 3.
- 5
First square −2 to get 4; then 2 × 4 − 3 = 5.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.