Answer:
A.) After adding 4 to both sides, the equation is
C.) The equation can be solved for x using exactly one more step by multiplying both sides by ![-\frac{3}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D)
D.) The equation can be solved for x using exactly one more step by dividing both sides by ![-\frac{2}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
The correct questions is as follows:
Carina begins to solve the equation -4-2/3x=-6 by adding 4 to both sides. Which statements regarding the rest of the solving process could be true? Check all that apply.
A.) After adding 4 to both sides, the equation is -2/3x=-2.
B.) After adding 4 to both sides, the equation is -2/3x=-10 .
C.) The equation can be solved for x using exactly one more step by multiplying both sides by -3/2.
D.) The equation can be solved for x using exactly one more step by dividing both sides by -2/3.
E.) The equation can be solved for x using exactly one more step by multiplying both sides by -2/3.
Given equation:
![-4-\frac{2}{3}x=-6](https://tex.z-dn.net/?f=-4-%5Cfrac%7B2%7D%7B3%7Dx%3D-6)
To show the steps we will carry out in order to solve for ![x](https://tex.z-dn.net/?f=x)
Solution:
Solving for ![x](https://tex.z-dn.net/?f=x)
Step 1:
Adding both sides by 4
![4-4-\frac{2}{3}x=-6+4](https://tex.z-dn.net/?f=4-4-%5Cfrac%7B2%7D%7B3%7Dx%3D-6%2B4)
Thus, we get:
![-\frac{2}{3}x=-2](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7Dx%3D-2)
Thus statement A is correct.
Step 2:
Multiplying both sides by ![-\frac{3}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D)
![-\frac{3}{2}\times -\frac{2}{3}x=-2\times -\frac{3}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D%5Ctimes%20-%5Cfrac%7B2%7D%7B3%7Dx%3D-2%5Ctimes%20-%5Cfrac%7B3%7D%7B2%7D)
Thus, we get:
[Two negatives multiply to give a positive]
This proves that statement C is correct.
Or Step 2:
Dividing both sides by ![-\frac{2}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D)
![\frac{-\frac{2}{3}x}{-\frac{2}{3}}=\frac{-2}{-\frac{2}{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B-%5Cfrac%7B2%7D%7B3%7Dx%7D%7B-%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Cfrac%7B-2%7D%7B-%5Cfrac%7B2%7D%7B3%7D%7D)
Thus, we get:
[On dividing with a fractional divisor, we take reciprocal and multiply it with the dividend.]
[Two negatives multiply to give a positive]
This prove that statement D is correct.