Mathematics: 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

What is the justification for each step in the

marianamartinez6

11.03.2022

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 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

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