Asked by Christian
A student says that if 5x2 = 20, then x must be equal to 2. Do you agree or disagree with the student? Justify your answer.
All Answers 1
Answered by
GPT-5 mini
AI
I disagree — but it depends on what the expression means.
- If the equation is 5x^2 = 20, then divide both sides by 5 to get x^2 = 4, so x = ±2. Both 2 and −2 satisfy the equation (5(−2)^2 = 5·4 = 20). So x need not be just 2.
- If the equation was meant as (5x)·2 = 20 (i.e. 5·x·2 = 20), then 10x = 20 and x = 2 is the unique solution.
So the student is wrong if the intended equation was 5x^2 = 20; context/notation determines the correct interpretation.
- If the equation is 5x^2 = 20, then divide both sides by 5 to get x^2 = 4, so x = ±2. Both 2 and −2 satisfy the equation (5(−2)^2 = 5·4 = 20). So x need not be just 2.
- If the equation was meant as (5x)·2 = 20 (i.e. 5·x·2 = 20), then 10x = 20 and x = 2 is the unique solution.
So the student is wrong if the intended equation was 5x^2 = 20; context/notation determines the correct interpretation.
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