In Step 2 have a mistake in student solution so the option B is correct answer.
In the given question,
A student solved the inequality [tex]\frac{-x+4}{3} > \frac{x+1}{2}[/tex].
We have to find the error in the student solution.
To find the mistake we first solve the give inequality.
The equality is [tex]\frac{-x+4}{3} > \frac{x+1}{2}[/tex]
To solve this equality we firstly equal the denominator by multiplying and divide 2 on left side and 3 on right side.
So [tex]\frac{2}{2}\times\frac{-x+4}{3} > \frac{x+1}{2}\times\frac{3}{3}[/tex]
Now simplifying
[tex]\frac{2(-x+4)}{6} > \frac{3(x+1)}{6}[/tex]
Now simplifying the brackets of numerator ob both side using distributive property.
In Distributive Property: a(b+c)=ab+bc
[tex]\frac{2\times(-x)+2\times4}{6} > \frac{3\times x+3\times1}{6}[/tex]
[tex]\frac{-2x+8}{6} > \frac{3x+3}{6}[/tex]
Since the both side have same numerator. So we can write the inequality as
-2x+8 > 3x+3
Subtract 8 on both side
-2x+8-8 > 3x+3-8
-2x > 3x-5
Subtract 3x on both side
-2x-3x > 3x-5-3x
-5x > -5
Divide by -5 on both side
-5/-5 x > -5/-5
x > 1
Hence the value of x is greater than 1.
Now we see the step on student.
We can see that in step 2 has mistake. In step 2 student doesn't use distributive property to solve the bracket.
Hence, we can say that option 2 is correct.
To learn more about Distributive Property link is here
https://brainly.com/question/5637942
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