Question

What is the justification for each step in the solution of the equation?

23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12 Distributive Property
2x=6x+13
−4x=13 Addition or Subtraction Property of Equality
x=−134

Answer 1

2/3x - 1/3 = 2(x + 2) Given

2x - 1 = 6(x + 2) Multiplication or Division Property of Equality

2x - 1 = 6x + 12 Distributive Property

2x = 6x + 13 Addition or Subtraction Property of Equality

-4x = 13 Addition or Subtraction Property of Equality

x = -13/4 Multiplication or Division Property of Equality

I took the test, you can trust these answer are correct.

Answer 2

For this case we have the following equation:

`(2)/(3)x-(1)/(3)= 2 (x + 2)\\`

If we multiply both sides of the equation by 3 we get:

`2x-1 = 6 (x + 2)` ---> Multiplication Property of Equality

Applying the distributive property we have:

`2x-1 = 6x + 12` ---> Distributive Property

Adding 1 on both sides of equality we have:

`2x-1 + 1 = 6x + 12 + 1\\`

`2x = 6x + 13` ---> Addition Property of Equality

Subtracting
`6x` on both sides we have:

`-6x + 2x = 6x-6x + 13\\`

`-4x = 13` ---> Subtraction Property of Equality

Finally, dividing by -4 on both sides we have:

`(-4x)/(-4)= (13)/(-4)\\`

`x = -(13)/(4)`---> Division Property of Equality