Question

now, rewrite the expression on the left without parentheses. we have 1 group of 6c + 4 in the numerator, which can just be written as 6c + 4. then, rewrite 2 in the denominator.
\\(\frac{\cancel{4} (6c + 4)}{\cancel{8}}\\) = \\(-2c + 4\\)
\\(\frac{\cancel{4} (6c + 4)}{\cancel{8}^2}\\) = \\(-2c + 4\\)
\\(\frac{\boxed{}}{\boxed{}}\\) = \\(-2c + 4\\)
4 \\(6c + 4\\) 8 2

Explanation:

Step1: Simplify the fraction

The original fraction is $\frac{4(6c + 4)}{8}$. We can simplify the numerator and the denominator by dividing both by 4. The numerator $4(6c + 4)\div4 = 6c + 4$, and the denominator $8\div4 = 2$. So the simplified fraction is $\frac{6c + 4}{2}$.

Step2: Set the simplified fraction equal to the right side

Now we have $\frac{6c + 4}{2}=-2c + 4$. Multiply both sides by 2 to eliminate the denominator: $6c + 4 = 2(-2c + 4)$.

Step3: Expand the right side

Expand $2(-2c + 4)$ to get $-4c + 8$. So the equation becomes $6c + 4=-4c + 8$.

Step4: Add $4c$ to both sides

Adding $4c$ to both sides gives $6c + 4c+ 4=-4c + 4c+ 8$, which simplifies to $10c + 4 = 8$.

Step5: Subtract 4 from both sides

Subtract 4 from both sides: $10c + 4 - 4=8 - 4$, so $10c = 4$.

Step6: Divide both sides by 10

Divide both sides by 10: $c=\frac{4}{10}=\frac{2}{5}=0.4$. But first, for the blanks, the numerator is $6c + 4$ and the denominator is 2.

Answer:

The numerator is $6c + 4$ and the denominator is 2. If we are to solve for $c$, the value of $c$ is $\frac{2}{5}$ (or 0.4). For the blanks in the problem (rewriting the fraction), the top blank is $6c + 4$ and the bottom blank is 2.