Question

Complete the statement about how you could solve the equation 2c−3=2(6−c)+ 7c .

Distribute and collect like terms on each side, , 1 of 3.
Select Choice
a.12 from each side, , 2 of 3.
b.2c from each side, then , 3 of 3.
c.each side by 3.

Answer 1

To solve the equation 2c−3=2(6−c)+7c, you must distribute the 2, combine like terms, subtract 2c from each side, and finally, subtract 12 and divide by 3 to isolate and solve for c.

Step-by-step explanation:

To solve the equation 2c−3=2(6−c)+7c, we need to distribute and collect like terms on each side. Let's break down the steps involved in solving this equation:

1. Distribute the 2 in 2(6−c) to obtain 12 - 2c.
2. Combine like terms on each side. On the left, we have 2c, and on the right, we have −2c + 7c. Adding −2c and 7c gives us 5c.
3. The equation now looks like 2c - 3 = 12 + 5c. To isolate c, subtract 2c from each side, leading to -3 = 12 + 3c.
4. Finally, subtract 12 from each side to obtain −3 - 12 = 3c, which simplifies to −15 = 3c.
5. Divide each side by 3 to find the value of c, resulting in c = −5.

After finding the value for c, we should check the answer to ensure it is reasonable by plugging it back into the original equation.