Answer:
- correct answer is C
- Haley incorrectly applied the distributive property
Step-by-step explanation:
If you simplify the given equation, you find it matches choice C.
[tex]\dfrac{1}{2}(6-x)+3x=\dfrac{1}{2}x-8\\\\3-\dfrac{1}{2}x+3x=\dfrac{1}{2}x-8\\\\3+\dfrac{5}{2}x=\dfrac{1}{2}x-8\qquad\text{matches choice C}[/tex]
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Haley's error seems to be failing to distribute the 1/2 properly when she eliminated parentheses. Apparent, she incorrectly decided that ...
1/2(6 -x) ⇒ 3 -x . . . . instead of 3 -1/2x
Then when -x was added to +3x, she got 2x. Had she done it properly, she would have added -1/2x to +3x to get 5/2x.
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Additional comment
It is a common error to "distribute" the factor outside parentheses to the first term only, as Haley apparently did. Another common error is to fail to distribute minus signs properly. The distributive property requires you apply the outside factor to all of the terms inside parentheses.
