Question

the equation $9(x + 7)=27$ is solved in several steps below. for each step, choose the reason that best justifies it. step reason $9(x + 7)=27$ given equation $9x + 63 = 27$ \choose one\ $9x + 63 - 63 = 27 - 63$ addition property of equality subtraction property of equality $9x = -36$ multiplication property of equality division property of equality $\frac{9x}{9}=\frac{-36}{9}$ simplifying distributive property $x = -4$

Explanation:

Step1: Match step to property

$9(x+7)=27 \to 9x+63=27$ uses $a(b+c)=ab+ac$.

Step2: Match step to property

$9x+63-63=27-63$ subtracts 63 from both sides.

Step3: Match step to property

$9x+63-63=27-63 \to 9x=-36$ simplifies the equation.

Step4: Match step to property

$9x=-36 \to \frac{9x}{9}=\frac{-36}{9}$ divides both sides by 9.

Step5: Match step to property

$\frac{9x}{9}=\frac{-36}{9} \to x=-4$ simplifies the equation.

Answer:

Step	Reason
$9x+63=27$	Distributive Property
$9x+63-63=27-63$	Subtraction Property of Equality
$9x=-36$	Simplifying
$\frac{9x}{9}=\frac{-36}{9}$	Division Property of Equality
$x=-4$	Simplifying