Final answer:
To solve the given equation using the distributive property, we apply the property to both sides of the equation and simplify. After combining like terms and isolating the variable, we solve for c by dividing both sides of the equation. The solution is c = 4.
Step-by-step explanation:
The given equation is 60 - (2c + 4) = 4(c + 7) + c. We can simplify this equation using the distributive property, which states that multiplication can be distributed over terms in summation.
Applying the distributive property to both sides of the equation, we get 60 - 2c - 4 = 4c + 28 + c.
Simplifying further gives us 56 - 2c = 5c + 28.
To solve for c, we can combine like terms by adding 2c to both sides of the equation:
56 - 2c + 2c = 5c + 28 + 2c.
This simplifies to 56 = 7c + 28.
Next, we can isolate the variable by subtracting 28 from both sides of the equation:
56 - 28 = 7c + 28 - 28.
This leaves us with 28 = 7c.
Finally, we can solve for c by dividing both sides of the equation by 7: 28/7 = 7c/7. The simplified solution is c = 4.
Learn more about Solving equations using the distributive property