Question

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? Select three options.

Answer 1

Explanation:

A C D

Answer 2

A.) After adding 4 to both sides, the equation is
`-(2)/(3)x=-2`

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)`

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-(2)/(3)x=-6`

To show the steps we will carry out in order to solve for
`x`

Solution:

Solving for
`x`

Step 1:

Adding both sides by 4

`4-4-(2)/(3)x=-6+4`

Thus, we get:

`-(2)/(3)x=-2`

Thus statement A is correct.

Step 2:

Multiplying both sides by
`-(3)/(2)`

`-(3)/(2)* -(2)/(3)x=-2* -(3)/(2)`

Thus, we get:

`x=3` [Two negatives multiply to give a positive]

This proves that statement C is correct.

Or Step 2:

Dividing both sides by
`-(2)/(3)`

`(-(2)/(3)x)/(-(2)/(3))=(-2)/(-(2)/(3))`

Thus, we get:

`x=-2* -(3)/(2)` [On dividing with a fractional divisor, we take reciprocal and multiply it with the dividend.]

`x=3` [Two negatives multiply to give a positive]

This prove that statement D is correct.