LEARNER JOURNEY LABSUse inverse operations on both sides of an equation and verify the result in the original equation.
Standalone concept packageNo prior equation-solving skill is assumed. Arithmetic operations, variables, equality, and every new algebra decision are explained on this page.
Use inverse operations on both sides of an equation and verify the result in the original equation.
Construct the reasoning path, solve at least 4 of 5 mastery problems, and revise an unfamiliar explanation.
Inverse operations undo one another. Applying the same valid operation to both sides preserves equality while removing an operation from the variable.
This is the logic beneath every linear-solving step, including steps people sometimes describe informally as moving a term.
Move from left to right. Each decision prepares the next one; on a phone, follow the numbered cards from top to bottom.
Choose the equality-preserving path for x/3 + 4 = 9.
The reasoning path changes as each decision is selected.
Every example identifies the goal, explains the next move, carries out the algebra, and checks or interprets the result.
Predict first. Then use the visual relationship and reasoned feedback to check two decisions.
1. Which operation undoes adding 8?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
2. Which operation undoes multiplying by 5?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
A prompt supplies part of the reasoning. Predict the missing mathematical move before choices appear.
1. Why must the same operation be performed on both sides?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Solve all six. Use the specific feedback to revise a method or sign error.
1. After solving x + 6 = 14 as x = 8, what is the best check?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
2. What is the inverse of subtracting 3?
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3. What is the inverse of dividing by 4?
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4. Which step preserves 2x + 3 = 11?
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5. If a check gives 12 = 12, what does that show?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
6. If a check gives 7 = 10, what does that show?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Attempt all five. At least four correct answers are required for mastery.
1. Which is a legal equality-preserving step from x/3 = 5?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
2. Why is checking in the original equation stronger than checking only the final line?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
3. What property justifies adding the same number to both sides?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
4. What property justifies dividing both sides by the same nonzero number?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
5. Which habit best prevents sign errors?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Explain why performing an operation on only one side usually changes the solution set.
Judge the locked first attempt against every criterion. Each judgment gives revision guidance.
Equal expressions remain equal only when compatible changes are made to both. From x + 2 = 7, subtracting 2 from both sides gives x = 5. Subtracting 2 only on the left creates x = 7, a different and false claim. The same operation on both complete sides preserves the original solution.
The record reveals exact answers and model reasoning only after the corresponding attempt or self-check has occurred.