Question

Part A: Solve the equation 5(x + 2) = 6x + 3x − 14, 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

Answer 1

x = 6

Explanation:

Step 1 - Expand brackets via distributive property:

`5(x + 2) = 6x + 3x - 14\\5(x) + 5(2) = 6x + 3x - 14\\5x + 10 = 6x + 3x - 14`

Step 2 - Combine like terms:

`5x + 10 = 6x + 3x - 14\\5x + 10 = 9x - 14`

Step 3 - Use the addition property of equality to isolate the 9x:

`5x + 10 = 9x - 14\\5x + 10 + 14 = 9x - 14 + 14\\5x + 24 = 9x`

Step 4 - Use the subtraction property of equality to move the 5x over and isolate the 24:

`5x + 24 = 9x\\5x + 24 - 5x = 9x - 5x\\24 = 4x`

Step 5 - Use the division property of equality to simplify:

`4x = 24\\\\(4x)/(4) = (24)/(4)\\\\x = 6`

Hope this helps!