Equations with Parentheses Worksheet- Practice Problems and Answers
What Are Equations with Parentheses?
Equations with parentheses are algebraic expressions where the distributive property needs to be applied before solving. The parentheses indicate you multiply everything inside by the term outside before isolating the variable.
These equations look like this:
3(x + 4) = 21
Or like this:
5(2x - 3) + 7 = 32
If you don't know how to handle the parentheses first, you'll get the wrong answer every time. That's why worksheets focused on this skill matter.
How to Solve Equations with Parentheses
Here's the process:
- Apply the distributive property — multiply the term outside the parentheses by each term inside
- Combine like terms if any exist
- Move variables to one side of the equation
- Move constants to the other side
- Divide or multiply to isolate the variable
The Distributive Property Explained
The distributive property states:
a(b + c) = ab + ac
So for 2(x + 5), you calculate 2x + 10.
For 3(2x - 4), you calculate 6x - 12.
That's it. No shortcuts. Multiply everything inside by the number outside.
Practice Problems with Answers
Work through these problems. Check your answers at the end. If you get stuck, reread the distributive property section above.
Level 1: Basic Problems
Problem 1: Solve for x: 2(x + 3) = 14
Answer:
- Apply distributive property: 2x + 6 = 14
- Subtract 6 from both sides: 2x = 8
- Divide by 2: x = 4
Problem 2: Solve for x: 5(x - 2) = 25
Answer:
- Apply distributive property: 5x - 10 = 25
- Add 10 to both sides: 5x = 35
- Divide by 5: x = 7
Problem 3: Solve for x: 4(3x + 1) = 28
Answer:
- Apply distributive property: 12x + 4 = 28
- Subtract 4 from both sides: 12x = 24
- Divide by 12: x = 2
Level 2: Intermediate Problems
Problem 4: Solve for x: 3(2x + 5) + 4 = 31
Answer:
- Apply distributive property: 6x + 15 + 4 = 31
- Combine like terms: 6x + 19 = 31
- Subtract 19 from both sides: 6x = 12
- Divide by 6: x = 2
Problem 5: Solve for x: 7(2x - 3) - 5 = 16
Answer:
- Apply distributive property: 14x - 21 - 5 = 16
- Combine like terms: 14x - 26 = 16
- Add 26 to both sides: 14x = 42
- Divide by 14: x = 3
Problem 6: Solve for x: 4(3x + 2) = 8x + 24
Answer:
- Apply distributive property: 12x + 8 = 8x + 24
- Subtract 8x from both sides: 4x + 8 = 24
- Subtract 8 from both sides: 4x = 16
- Divide by 4: x = 4
Level 3: Advanced Problems
Problem 7: Solve for x: 5(2x + 3) - 3(4x - 1) = 18
Answer:
- Apply distributive property to both: 10x + 15 - 12x + 3 = 18
- Combine like terms: -2x + 18 = 18
- Subtract 18 from both sides: -2x = 0
- Divide by -2: x = 0
Problem 8: Solve for x: 2(3x + 4) + 5(2x - 1) = 41
Answer:
- Apply distributive property to both: 6x + 8 + 10x - 5 = 41
- Combine like terms: 16x + 3 = 41
- Subtract 3 from both sides: 16x = 38
- Divide by 16: x = 38/16 = 19/8 = 2.375
Common Mistakes to Avoid
These errors show up constantly. Don't make them:
- Forgetting to distribute — only multiplying the first term inside the parentheses. Wrong: 3(x + 5) = 3x + 5. Right: 3(x + 5) = 3x + 15.
- Dropping negative signs — when distributing a negative number, both terms change. Wrong: -2(x - 3) = -2x - 6. Right: -2x + 6.
- Skipping the combination step — after distributing, you must combine like terms before isolating the variable.
- Dividing unevenly — when dividing both sides by a number, divide every term. Not just the variable.
Signs You Need More Practice
- You consistently forget to distribute to both terms
- You mix up when to add and when to subtract
- You solve for x but your answer doesn't check out when plugged back in
- You've avoided these problems and now you're behind
If any of this describes you, worksheets are exactly what you need. The only way to get faster is to do more problems.
How to Use These Worksheets Effectively
Don't just skim the problems. Actually solve them.
- Set a timer — 15-20 minutes of focused work beats an hour of distracted glancing
- Show your work — write every step. The process matters more than the answer
- Check immediately — don't wait until the end to verify. Check each problem as you finish
- Redo wrong answers — if you got one wrong, solve it again without looking at the solution first
- Track your mistakes — write down what went wrong so you don't repeat it
Comparing Worksheet Types
| Type | Best For | Drawback |
|---|---|---|
| Basic drills | Learning the distributive property | Can feel repetitive |
| Multi-step problems | Building complexity tolerance | Harder to isolate errors |
| Word problems | Application skills | Can obscure the math |
| Timed assessments | Speed practice | Promotes rushing mistakes |
| Error analysis tasks | Deep understanding | Requires teacher guidance |
Start with basic drills. Move to multi-step once you can finish basic problems without thinking. Only add word problems when the mechanics are solid.
Where to Find Quality Worksheets
Skip the generic worksheet generators that spit out random problems. Look for:
- Worksheets with graded difficulty levels
- Problems that include step-by-step answer keys
- Variety in problem structure, not just different numbers
- Negative number practice included
Your textbook probably has decent problems. Khan Academy offers free practice sets. Your teacher's worksheets are usually better than random internet finds because they align with what you're actually learning.
Final Warning
Equations with parentheses are a gatekeeper topic. If you can't solve these reliably, you'll struggle with everything that follows — fractions, polynomials, quadratic equations. The distributive property doesn't go away. It becomes the foundation for everything else.
Don't skip the practice. Don't assume you'll figure it out later. Get it right now.