A pupil expands 3(x + 4) as 3x + 4. Correct it.
Answer and explanation
3x + 12. The factor 3 multiplies both terms.
3x + 12. The factor 3 multiplies both terms.
Subjects
Algebra
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Sample exercises
A pupil says (x + 5)² = x² + 25. What is missing?
Answer and explanation
The middle term 10x is missing: (x + 5)² = x² + 10x + 25.
The middle term 10x is missing: (x + 5)² = x² + 10x + 25.
A pupil combines 2x + 3x² as 5x³. Explain the error.
Answer and explanation
x and x² are unlike terms and cannot be added by adding exponents; the expression remains 3x² + 2x.
x and x² are unlike terms and cannot be added by adding exponents; the expression remains 3x² + 2x.
Solve 4x − 7 = 21.
Answer and explanation
7
4x = 28, so x = 7.
Solve 5x + 2 = 3x + 18.
Answer and explanation
8
2x = 16, so x = 8.
Solving −2x > 6 gives
- x > −3
- x > 3
- x < 3
- x < −3
Answer and explanation
x < −3
x < −3
Study notes
Substitute into an expression
Substitute with brackets, then follow the order of operations.
Grades 6–9Combine like terms
Only terms with the same variable part can be combined this way.
Grades 6–9Equations with x on both sides
Perform the same operation on both sides. Here a is different from c.
Grades 8–10Simultaneous equations
Add the equations to eliminate y, then solve for x.
Grades 9–11Inverse linear functions
Undo addition first, then undo multiplication.
Grades 8–11Compose two functions
Apply the inside function first.
Grades 9–12Algebra · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 6–8Algebra · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 9–10Algebra · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 11–12Find the mistake: algebra
Apply the same valid operation to both sides and respect restrictions such as division by zero.
Grades 8–11Find the mistake: algebra · revision card
Apply the same valid operation to both sides and respect restrictions such as division by zero.
Grades 8–11Functions: domains and transformations
Over real numbers, denominators cannot be zero and even-root inputs must be nonnegative.
Grades 10–12Functions: domains and transformations · revision card
Over real numbers, denominators cannot be zero and even-root inputs must be nonnegative.
Grades 10–12Expressions, equations and structure
Simplifying an expression and solving an equation are different tasks.
Grades 6–9Expressions, equations and structure · Revision card
Simplifying an expression and solving an equation are different tasks.
Grades 6–9Functions, domains and inverse reasoning
A function assigns exactly one output to each allowed input.
Grades 9–12Functions, domains and inverse reasoning · Revision card
A function assigns exactly one output to each allowed input.
Grades 9–12Equations, expressions and equivalent steps
Preserve equality and check a solution in the original equation.
Grades 6–9Equations, expressions and equivalent steps · Revision sheet
Preserve equality and check a solution in the original equation.
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