(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

Equation: 7x+3x-18=6(x+3).

1.) Use SADMEP as the order of operations.

2.) First, Distributive Property: 6(x+3)=6x+18

7x+3x-18=6x+18.

3.) Combine Like Terms: 7x+3x= 10x.

10x-18=6x+18.

4.) Addition Property of Equality (Also an Inverse Operation) to Combine Like Terms: 10x=6x+36. We +18 to -18 on the left side of the = to cancel the term out and moved it to the right side of the =, which added with the other 18. 18+18=36.

10x=6x+36.

5.) Subtraction Property of Equality (also an inverse property) to combine like terms. We subtracted 6x from the right side of the =, and subtracted it to 10x on the left side of the = to cancel the 6x out and subtracted from the 10x. 10x-6x=4x.

4x=36.

6.) We will use the Division property (also an inverse property) of Equality to divide 4x from both sides to isolate X. 4x/4=36/4.

Therefore. X=9.

Now, we can use the Substitution Property of Equality to substitute X into our most simplified form of the equation to check our answer. 4(9)=36. So, X is correct as 9.

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