Question

Which of the following equations is equivalent to

Answer 1

none

Explanation:

We can start by multiplying both side of the equation by 6 in order to remove the fractions.

`6*(x+3)/(3) = 6(5 - (x-3)/(6))`

`2(x + 3) = 30 - 6*(x-3)/(6)`

`2x + 6 = 30 -(x - 3)`

`2x + 6 = 30 - x + 3`

Now, we can try to see if this equation is equivalent to the other options.

Every option has the left side as 2x - 6. In order to get that, we need to subtract 12 on both sides:

`2x - 6 = 30 - x + 3 - 12`

This simplifies to

`2x-6 = 18 - x + 3`

This is not the same as any of the options shown.

We can check this by solving the equations.

2x - 6 = 18 - x + 3

3x = 6 + 18 + 3

3x = 27

x = 9

Now, the first option:

2x - 6 = 10 - x - 3

3x = 6 + 10 - 3

3x = 13

x = 13/3

The second option is the exact same as the third, so they would have the same solution:

2x - 6 = 30 - x- 3

3x = 6 + 30 - 3

3x= 33

x = 11

Since none of the options have the answer 9, they are not equivalent to the equation shown.

Answer 2

Explanation:

`(x+3)/(3) =5- (x-3)/(6) \\((x+3)/(3)) *6 =5 - (x-3)`

`2x+6 = 5 - x+3`