Question

(01.02 mc)
part a: solve the equation 7x + 3x - 18 = 6(x + 3), and show your work. (5 points)
part b: use this list of properties to justify each step of your math work. justifications may be used more than once if needed. (5 points)
distributive property
subtraction property of equality
combine like terms
multiplication property of equality
division property of equality
given
addition property of equality

Explanation:

Step1: Combine like - terms on left side

Given the equation $7x + 3x-18=6(x + 3)$. First, combine $7x$ and $3x$ on the left - hand side.
$7x+3x=10x$, so the equation becomes $10x-18 = 6(x + 3)$. Justification: Combine Like Terms.

Step2: Apply distributive property

Expand the right - hand side using the distributive property $a(b + c)=ab+ac$. Here, $a = 6$, $b=x$, and $c = 3$. So, $6(x + 3)=6x+18$. The equation is now $10x-18=6x + 18$. Justification: Distributive Property.

Step3: Subtract $6x$ from both sides

Subtract $6x$ from both sides of the equation $10x-18=6x + 18$.
$10x-6x-18=6x-6x + 18$, which simplifies to $4x-18=18$. Justification: Subtraction Property of Equality.

Step4: Add 18 to both sides

Add 18 to both sides of the equation $4x-18=18$.
$4x-18 + 18=18+18$, resulting in $4x=36$. Justification: Addition Property of Equality.

Step5: Divide both sides by 4

Divide both sides of the equation $4x=36$ by 4.
$\frac{4x}{4}=\frac{36}{4}$, so $x = 9$. Justification: Division Property of Equality.

Answer:

$x = 9$