Question

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.42-(2c+4)=4(c+6)+c

Answer 1

Let's solve your equation step-by-step.

42−(2c+4)=4(c+6)+c

Step 1: Simplify both sides of the equation.

42−(2c+4)=4(c+6)+c

42+−1(2c+4)=4(c+6)+c(Distribute the Negative Sign)

42+−1(2c)+(−1)(4)=4(c+6)+c

42+−2c+−4=4(c+6)+c

42+−2c+−4=(4)(c)+(4)(6)+c(Distribute)

42+−2c+−4=4c+24+c

(−2c)+(42+−4)=(4c+c)+(24)(Combine Like Terms)

−2c+38=5c+24

−2c+38=5c+24

Step 2: Subtract 5c from both sides.

−2c+38−5c=5c+24−5c

−7c+38=24

Step 3: Subtract 38 from both sides.

−7c+38−38=24−38

−7c=−14

Step 4: Divide both sides by -7.

−7c/-7 = -14/-7

c=2

Answer:

c=2

the distributive property makes this possible because it helps break down the equation.