Question

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

Answer 1

For this case we have the following equation:

$\frac{2}{3}x-\frac{1}{3}= 2 (x + 2)$

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:

$\frac{-4x}{-4}= \frac{13}{-4}$

$x = -\frac{13}{4}$---> Division Property of Equality

Answer 2

Answer:

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.