Answer:
No, the student's work is not correct.
Step-by-step explanation:
Given : Student expanded an expression, as shown.
![-6(4x-\frac{2}{13} )](https://tex.z-dn.net/?f=-6%284x-%5Cfrac%7B2%7D%7B13%7D%20%29)
![-6(4x)+6(-\frac{2}{13} )](https://tex.z-dn.net/?f=-6%284x%29%2B6%28-%5Cfrac%7B2%7D%7B13%7D%20%29)
![-24x-\frac{12}{13}](https://tex.z-dn.net/?f=-24x-%5Cfrac%7B12%7D%7B13%7D)
To find : Is the student's work correct?
Solution :
The expansion of student is not correct.
Follow the below steps to get correct solution and student mistake,
Step 1 - Write the expression,
![-6(4x-\frac{2}{13} )](https://tex.z-dn.net/?f=-6%284x-%5Cfrac%7B2%7D%7B13%7D%20%29)
Step 2 - Apply distributive property, ![a(b+c)=ab+ac](https://tex.z-dn.net/?f=a%28b%2Bc%29%3Dab%2Bac)
![=(-6)(4x)+(-6)(-\frac{2}{13})](https://tex.z-dn.net/?f=%3D%28-6%29%284x%29%2B%28-6%29%28-%5Cfrac%7B2%7D%7B13%7D%29)
Step 3 - Solve,
![=-24x+\frac{12}{13}](https://tex.z-dn.net/?f=%3D-24x%2B%5Cfrac%7B12%7D%7B13%7D)
The student was mistaken in step 2 in solving the sign.