Question

solve the equation for y. justify each step.
equation: (12 - 3y = 30x + 6)
explanation: write the equation.
reason: given

equation: (-3y = 30x - 6)
explanation:
reason: subtraction property of equality

equation:
explanation:
reason: division property of equality

options for equations: (y = 10x - 2), (y = -10x + 2), (6 - 3y = 30x)
options for explanations: subtract 12 from each side, divide each side by 2, divide each side by -3)

Explanation:

Step1: Write original equation

$12 - 3y = 30x + 6$

Step2: Subtract 12 from both sides

$-3y = 30x + 6 - 12$
$-3y = 30x - 6$

Step3: Divide by -3 on both sides

$y = \frac{30x - 6}{-3}$
$y = -10x + 2$

Answer:

Equation	Explanation	Reason
$-3y = 30x - 6$	Subtract 12 from each side.	Subtraction Property of Equality
$y = -10x + 2$	Divide each side by $-3$.	Division Property of Equality

Final solved form: $y = -10x + 2$