Question

solve the equation below. what’s the value of c?
divide 4 and 8 by the common factor of 4 to rewrite this equation.
\frac{\cancel{4} (6c + 4)}{\cancel{8}} = -2c + 4

Explanation:

Step1: Simplify the fraction

Divide 4 by 4 (result is 1) and 8 by 4 (result is 2). So the equation becomes $\frac{1\times(6c + 4)}{2}=-2c + 4$.

Step2: Multiply both sides by 2

Multiply both sides of the equation $\frac{6c + 4}{2}=-2c + 4$ by 2 to get rid of the denominator: $6c + 4 = 2\times(-2c + 4)$.

Step3: Expand the right side

Expand $2\times(-2c + 4)$: $6c + 4=-4c + 8$.

Step4: Add 4c to both sides

Add 4c to both sides: $6c + 4c+ 4=-4c + 4c+ 8$, 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 by 10

Divide both sides by 10: $c=\frac{4}{10}=\frac{2}{5}$.

Answer:

The value of \( c \) is \(\frac{2}{5}\) (or 0.4). The simplified fraction numerator is 1 and denominator is 2.