Question

Reasoning Use the Distributive Property to solve the equation below. Use pencil and paper. Explain why the Distributive Property makes it possible to solve this equation. 44 - (2c + 3) = 4(C+5) + C The solution of the equation is

Answer 1

Using the Distributive Property, we solved the equation 44 - (2c + 3) = 4(C + 5) + C by distributing multiplication over addition and subtraction, combining like terms, and isolating the variable to find c = 3.

Step-by-step explanation:

The student is asked to use the Distributive Property to solve the equation 44 - (2c + 3) = 4(C + 5) + C. The Distributive Property states that A(B+C) = AB + AC, which allows us to simplify or expand expressions by distributing the multiplication over addition or subtraction within the brackets.

First, apply the Distributive Property to both sides of the equation:

• Left side: 44 - 2c - 3
• Right side: 4c + 20 + C

Combine like terms and simplify:

• 41 - 2c = 4c + 20 + C
• 41 - 2c = 5c + 20

Then, you move all the c terms to one side and the constant terms to the other side:

• 41 - 20 = 5c + 2c
• 21 = 7c

Finally, divide both sides by 7 to solve for c:

• c = 3

The solution of the equation is c = 3.