Solve and verify linear equations
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Solve x + 4 = 7.
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Answer: 3
- Reverse the operations while preserving equality on both sides.
- The solution is x = 3. Substitution check: 3 + 4 = 7.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Undo operations systematically and check natural-number solutions.
Read the official VCAA curriculum description (VC2M7A03)
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Activities to practise beyond the quiz
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M7A03-C01Solving an equation means finding a variable value that makes its two sides equal. Undo addition with subtraction and multiplication with division, preserving the same relationship on both sides.
- VC2M7A03-C02For 3x + 7 = 19, remove 7 first, then divide by 3 to get x = 4. With a bracket, treat the whole bracket as a quantity before solving for its inner unknown.
- VC2M7A03-C03Substitute the proposed natural-number solution into every original term. If variables appear on both sides, collect equal variable terms before reversing the remaining operations. An incorrect trial can reveal exactly which step used the wrong inverse.
- VC2M7A03-C04Demonstrating an equation-solving process and communicating substitution checks.
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Subskills
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Descriptor-derived subskills
- D01Preserve an equalitySolving an equation means finding a variable value that makes its two sides equal. Undo addition with subtraction and multiplication with division, preserving the same relationship on both sides.
- D02Reverse a sequence of operationsFor 3x + 7 = 19, remove 7 first, then divide by 3 to get x = 4. With a bracket, treat the whole bracket as a quantity before solving for its inner unknown.
- D03Verify in the original equationSubstitute the proposed natural-number solution into every original term. If variables appear on both sides, collect equal variable terms before reversing the remaining operations. An incorrect trial can reveal exactly which step used the wrong inverse.