Equations with brackets can be solved by expanding with the distributive law, collecting like terms and using inverse operations. Every operation must be applied to both sides to preserve equality.
Example
For 3(x + 4) = 27, expand to 3x + 12 = 27, subtract 12, then divide by 3: x = 5.
Key terms
Expand:
Remove brackets by multiplying every term inside.
Distributive law:
The rule a(b + c) = ab + ac.
Inverse operation:
An operation that undoes another operation.
Questions
1. What does Expand mean?
The rule a(b + c) = ab + ac.
Remove brackets by multiplying every term inside.
An operation that undoes another operation.
A value selected without mathematical context.
2. Which statement correctly describes Distributive law?
Remove brackets by multiplying every term inside.
An operation that undoes another operation.
The rule a(b + c) = ab + ac.
A step that removes the need to calculate.
3. Which definition matches Inverse operation?
An operation that undoes another operation.
Remove brackets by multiplying every term inside.
The rule a(b + c) = ab + ac.
A label that can be ignored when solving.
4. Which worked example belongs to solving equations with brackets?
An example that changes the given values before starting.
An example that gives a result without a mathematical method.
Multiplying only the first term inside a bracket instead of every term.
For 3(x + 4) = 27, expand to 3x + 12 = 27, subtract 12, then divide by 3: x = 5.
5. Which practice approach is most reliable?
Expand the brackets, collect like terms and isolate the variable one valid step at a time.
Multiplying only the first term inside a bracket instead of every term.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
6. Which action is a sensible accuracy check?
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Substitute the solution into the original bracketed equation and compare both sides.
Change the units after calculating without using a conversion.
7. Where could solving equations with brackets be applied?
In a situation with no quantities or relationships.
Model equal-cost packages or repeated groups with a bracketed equation.
Only in a memorised classroom example.
In place of reading the conditions of a problem.
8. A student is beginning a solving equations with brackets problem. What should they do?
Multiplying only the first term inside a bracket instead of every term.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
Expand the brackets, collect like terms and isolate the variable one valid step at a time.
9. Which mistake is most important to avoid here?
Writing down the units supplied in the question.
Multiplying only the first term inside a bracket instead of every term.
Showing intermediate working.
Checking the result using the original information.
10. After calculating, which step gives the strongest evidence that the result is valid?
Substitute the solution into the original bracketed equation and compare both sides.
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Change the units after calculating without using a conversion.
11. Which task transfers this mathematics into a meaningful context?
Copy a completed answer without its method.
List unrelated numbers from the question.
Model equal-cost packages or repeated groups with a bracketed equation.
Repeat a definition without using it.
12. Why is the worked solving equations with brackets example valid?
It avoids the defining relationship in the topic.
Equations with brackets can be solved by expanding with the distributive law, collecting like terms and using inverse operations. Every operation must be applied to both sides to preserve equality.
It treats every numerical operation as interchangeable.
It relies on the answer being visually complicated.
13. Which statement best connects Expand and Distributive law?
Expand and Distributive law are unrelated labels.
Expand removes the need for Distributive law.
The meanings of Expand and Distributive law can be swapped.
Remove brackets by multiplying every term inside. The rule a(b + c) = ab + ac.
14. Which response shows mathematical reasoning rather than guessing?
Expand the brackets, collect like terms and isolate the variable one valid step at a time. Then substitute the solution into the original bracketed equation and compare both sides.
Multiplying only the first term inside a bracket instead of every term.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
15. Which explanation would best justify a final answer?
The answer must be right because it was completed quickly.
The method does not need to match the quantities or conditions.
Equations with brackets can be solved by expanding with the distributive law, collecting like terms and using inverse operations. Every operation must be applied to both sides to preserve equality. The result can be checked by this step: Substitute the solution into the original bracketed equation and compare both sides.
A different result was ignored because it was inconvenient.
16. A result seems unreasonable. What is the best diagnostic response?
Keep the result and remove the working.
Check for this common error: Multiplying only the first term inside a bracket instead of every term. Then substitute the solution into the original bracketed equation and compare both sides.
Change the original question so the result fits.
Choose a new answer without revisiting the method.
17. Which plan would produce the clearest solution for another reader?
Multiplying only the first term inside a bracket instead of every term.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
Expand the brackets, collect like terms and isolate the variable one valid step at a time. Show the working clearly and label the final result.
18. Which check is most closely tied to the mathematics in this topic?
Substitute the solution into the original bracketed equation and compare both sides.
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Change the units after calculating without using a conversion.
19. Which application requires the ideas from this topic?
A task with no measurable information or decision.
A task that forbids using the stated mathematical relationship.
Model equal-cost packages or repeated groups with a bracketed equation.
A task solved by copying an unrelated formula.
20. Which critique identifies a genuine flaw in a solution?
The solution states the relevant units.
Multiplying only the first term inside a bracket instead of every term.
The solution shows an intermediate step.
The solution checks its answer.
21. What is the strongest summary of solving equations with brackets?
It is a topic where units, conditions and checks never matter.
It is solved by choosing any operation that gives a whole number.
It has no connection to mathematical reasoning or real situations.
Equations with brackets can be solved by expanding with the distributive law, collecting like terms and using inverse operations. Every operation must be applied to both sides to preserve equality.
Answer key (parent copy)
1. Remove brackets by multiplying every term inside.
2. The rule a(b + c) = ab + ac.
3. An operation that undoes another operation.
4. For 3(x + 4) = 27, expand to 3x + 12 = 27, subtract 12, then divide by 3: x = 5.
5. Expand the brackets, collect like terms and isolate the variable one valid step at a time.
6. Substitute the solution into the original bracketed equation and compare both sides.
7. Model equal-cost packages or repeated groups with a bracketed equation.
8. Expand the brackets, collect like terms and isolate the variable one valid step at a time.
9. Multiplying only the first term inside a bracket instead of every term.
10. Substitute the solution into the original bracketed equation and compare both sides.
11. Model equal-cost packages or repeated groups with a bracketed equation.
12. Equations with brackets can be solved by expanding with the distributive law, collecting like terms and using inverse operations. Every operation must be applied to both sides to preserve equality.
13. Remove brackets by multiplying every term inside. The rule a(b + c) = ab + ac.
14. Expand the brackets, collect like terms and isolate the variable one valid step at a time. Then substitute the solution into the original bracketed equation and compare both sides.
15. Equations with brackets can be solved by expanding with the distributive law, collecting like terms and using inverse operations. Every operation must be applied to both sides to preserve equality. The result can be checked by this step: Substitute the solution into the original bracketed equation and compare both sides.
16. Check for this common error: Multiplying only the first term inside a bracket instead of every term. Then substitute the solution into the original bracketed equation and compare both sides.
17. Expand the brackets, collect like terms and isolate the variable one valid step at a time. Show the working clearly and label the final result.
18. Substitute the solution into the original bracketed equation and compare both sides.
19. Model equal-cost packages or repeated groups with a bracketed equation.
20. Multiplying only the first term inside a bracket instead of every term.
21. Equations with brackets can be solved by expanding with the distributive law, collecting like terms and using inverse operations. Every operation must be applied to both sides to preserve equality.