What you will be able to do
- Work each problem without looking at the answer.
- Write the algebraic step that justifies each change.
- Check the result in the original relationship.
- Use the error notes to decide what to practise next.
How to use this worksheet
Solve in order. Keep both sides balanced, combine like terms before isolating the variable and substitute the result into the original equation.
- Undo operations in reverse order
- Distribute and combine like terms
- Handle variables on both sides
- Recognise no-solution and infinitely-many-solution equations
For a clean student copy, print this page and cover the worked solutions or select the problem pages in your browser’s print preview.
Practice problems
Problem 1
x + 7 = 19
Problem 2
5x = -35
Problem 3
3x - 8 = 16
Problem 4
4(x - 2) + 3 = 19
Problem 5
7x + 4 = 3x + 28
Problem 6
2(3x + 1) = 6x + 5
Answer key with worked solutions
Problem 1
x + 7 = 19
- 1.Subtract 7 from both sides: x = 12.
Answer: x = 12
Check: 12 + 7 = 19.
Problem 2
5x = -35
- 1.Divide both sides by 5: x = -7.
Answer: x = -7
Check: 5(-7) = -35.
Problem 3
3x - 8 = 16
- 1.Add 8: 3x = 24.
- 2.Divide by 3: x = 8.
Answer: x = 8
Check: 3(8) - 8 = 16.
Problem 4
4(x - 2) + 3 = 19
- 1.Distribute: 4x - 8 + 3 = 19.
- 2.Combine: 4x - 5 = 19.
- 3.Add 5 and divide by 4: x = 6.
Answer: x = 6
Check: 4(6 - 2) + 3 = 19.
Problem 5
7x + 4 = 3x + 28
- 1.Subtract 3x: 4x + 4 = 28.
- 2.Subtract 4: 4x = 24.
- 3.Divide by 4: x = 6.
Answer: x = 6
Check: 46 = 46.
Problem 6
2(3x + 1) = 6x + 5
- 1.Distribute: 6x + 2 = 6x + 5.
- 2.Subtract 6x: 2 = 5, a contradiction.
Answer: No solution
Check: The variable terms cancel and leave a false statement.
Use mistakes to choose the next step
Read why equations feel difficultPractise linear inequalities next
| If this happened | Likely issue | Next practice move |
|---|---|---|
| Sign changed incorrectly | Inverse operation or negative-number error | Write the same operation on both sides |
| Distribution missed a term | Parentheses error | Draw arrows from the multiplier to every term |
| Answer works in simplified line but not original | Earlier algebra error | Substitute into the original equation |
| Variable disappears | Identity or contradiction | Decide whether the remaining statement is always true or false |
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Useful answers
Frequently asked questions
How can I check a linear-equation answer?
Substitute the value into the original equation and confirm that both sides are equal.
Why do operations have to be done to both sides?
An equation states that two expressions are equal. Applying the same valid operation preserves that equality.
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Sources, scope and accuracy
The worked examples and practice questions on this page are original Cambridge Veritas learning materials, not released STAAR items. Curriculum and testing details can change; use the linked Texas Education Agency pages for current official information. Cambridge Veritas is not affiliated with or endorsed by TEA.