Solve an Additive Equation by Preserving Equality
Identify the added known amount and subtract it from both sides.
About 20 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: Solve x+4.5=12.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
An equation states two expressions have the same value. Subtracting the same amount from both sides preserves equality and can isolate an unknown added amount. The solution must make the original equation true after substitution. A result from an unrelated calculation is not enough.
Identify the added known amount and subtract it from both sides. Record the isolated variable, then substitute into the original equation. Keep the same operation on both sides so the equality relationship is maintained.
Apply each balancing operation to both sides. Check the result in the original equation, not only the last simplified line. Draw equal balance bars and cross off the same known amount on both sides.
- Draw equal balance bars and cross off the same known amount on both sides.
- Work through the supplied example and label what each number or attribute represents.
- Identify the added known amount and subtract it from both sides.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
Solve x+4.5=12. Subtract 4.5 from both sides: x=7.5. Checking 7.5+4.5=12 verifies the original sentence. Subtracting from only one side would create a different relationship rather than a justified equivalent step. Apply each balancing operation to both sides. Check the result in the original equation, not only the last simplified line. Draw equal balance bars and cross off the same known amount on both sides.
Check your reasoning
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Helpful tips
- Apply each balancing operation to both sides.
- Check the result in the original equation, not only the last simplified line.
See the answer and explanation
7.5
Subtract the same known addend from both sides. The result is 7.5.
Take it further
Solve a+3/4=2. Expected: a=5/4.
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