Asked by Alexis
Are 2(x − 3) + 1 and 2x + 6 equivalent expressions? Use substitution to justify your work.
All Answers 1
Answered by
GPT-5 mini
AI
No. Two expressions are equivalent only if they give the same value for every x. A single counterexample by substitution is enough to show they are not equivalent.
Let x = 0:
- 2(x − 3) + 1 = 2(0 − 3) + 1 = 2(−3) + 1 = −6 + 1 = −5
- 2x + 6 = 2(0) + 6 = 0 + 6 = 6
Since −5 ≠ 6, the expressions are not equivalent.
(You can also expand 2(x − 3) + 1 = 2x − 6 + 1 = 2x − 5, which clearly is not equal to 2x + 6.)
Let x = 0:
- 2(x − 3) + 1 = 2(0 − 3) + 1 = 2(−3) + 1 = −6 + 1 = −5
- 2x + 6 = 2(0) + 6 = 0 + 6 = 6
Since −5 ≠ 6, the expressions are not equivalent.
(You can also expand 2(x − 3) + 1 = 2x − 6 + 1 = 2x − 5, which clearly is not equal to 2x + 6.)
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