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)
e terms
distributive property
subtraction property of equality
combine like terms
multiplication property of equality
division property of equality
given
addition property of equality

The equation 7x + 3x - 18 = 6(x + 3) has been solved using the given properties and the value of "x" is found to be 9

Solution:

Given that we have to solve the equation 7x + 3x - 18 = 6(x + 3)

⇒ 7x + 3x - 18 = 6(x + 3)

Step 1: Combine like terms

⇒ 10x  - 18 = 6(x + 3)

Step 2: Distributive Property

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products

⇒ 10x  - 18 = 6x + 18

Step 3: Subtraction Property of Equality

The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same

⇒ 10x -18 - 6x = 6x + 18 - 6x

⇒ 10x - 18 -6x = 18

Step 4: Combining like terms

⇒ 4x - 18 = 18

Step 5: Addition Property of Equality

The property that states that if you add the same number to both sides of an equation, the sides remain equal

⇒ 4x - 18 + 18 = 18 + 18

⇒ 4x = 36

Step 6: Division Property of Equality

The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal.

⇒

⇒ x = 9

Thus the properties are used and x is equal to 9

x = 9

Step-by-step explanation:

7x + 3x - 18 = 6(x + 3)

10x - 18 = 6(x + 3)                  Add like terms

10x - 18 = 6x + 18                   Distribute 6 to x and 3

4x - 18 = 18                             Subtract 6x to both sides

4x = 36                                  Add 18 to both sides

x = 9                                      Divide 4 to both sides