Expand 5(2x − 3)
- Multiply 5 × 2x = 10x.
- Multiply 5 × (−3) = −15.
- The equivalent expression is 10x − 15.
The distributive property
Explain why a factor outside brackets multiplies every term inside.
Lesson 05 · Start where you need
Your learning goal
Expand expressions and use distribution to solve and check equations.
Multiplication reaches every term
Three identical groups of (2x + 4) contain six x-terms and twelve units altogether. In symbols, 3(2x + 4) = 6x + 12. The outside factor multiplies both terms. This follows from repeated addition and is not a rule about simply removing brackets.
Words worth knowing
- Inverse operation
- An operation that undoes another operation.
- Solution
- A value that makes the original equation true.
- Preservation of equality
- Changing both sides in a way that keeps the solution set.
1
Make the idea visible.
Predict a change, adjust one value, then explain what stayed the same.
Tile shapes distinguish symbols; their lengths do not set x’s value. Blue is positive; red is negative. Signs and labels also identify each term.
Keep the sign attached to the term
For 4(x − 3), distribute 4 to x and to −3: 4x − 12. With a negative outside factor, each product changes accordingly: −2(x − 5) = −2x + 10. Brackets around a substituted negative value help prevent losing a sign.
Use equivalent forms strategically
The factored form 3(x + 4) shows three equal groups. The expanded form 3x + 12 makes the total variable and constant parts explicit. Both describe the same value for every x. Choose a form that makes a calculation or a solution easier to explain.
Solve after expanding, then verify
For 2(x + 3) = 18, expand to 2x + 6 = 18. Subtract 6 on both sides and divide by 2 to get x = 6. Alternatively, divide the original equation by 2 first. Both methods are valid because both preserve equality. Check with 2(6 + 3) = 18.
Worked examples
Follow the reasoning.
Solve 3(x − 2) = 15
- Divide both sides by 3: x − 2 = 5.
- Add 2 to both sides: x = 7.
- Check: 3(7 − 2) = 3 × 5 = 15.
Try it with support
Show your thinking.
Expand −3(x + 2).
Give me a hint
Multiply −3 by each term.
Compare a worked response
−3x − 6
Both products are negative: −3 × x and −3 × 2.
Explain the error in 2(x + 5) = 2x + 5.
Give me a hint
Which term did not receive the factor?
Compare a worked response
The constant must also be multiplied by 2.
The correct expansion is 2x + 10.
Independent practice
Check your understanding.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
Choose a response, then use the explanation to check your reasoning. This is practice, not a school mark.
Go further
Keep the connections close.
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