Full solution

Q. Solve for

c

. Express your answer as a proper or improper fraction in simplest terms.

\newline

-\frac{2}{5} c+\frac{3}{4}=\frac{2}{5}

\newline

Answer:

c=

Isolate variable c: Isolate the term containing the variable c. $\newline$ To do this, we need to move the $(3/4)$ to the other side of the equation by subtracting $(3/4)$ from both sides. $\newline$ $-\frac{2}{5}c + \frac{3}{4} - \frac{3}{4} = \frac{2}{5} - \frac{3}{4}$ $\newline$ Simplifying the left side, we get: $\newline$ $-\frac{2}{5}c = \frac{2}{5} - \frac{3}{4}$
Find common denominator: Find a common denominator for the fractions on the right side of the equation. $\newline$ The common denominator for $5$ and $4$ is $20$ . $\newline$ So we convert $(\frac{2}{5})$ and $(\frac{3}{4})$ to have the denominator of $20$ : $\newline$ $(\frac{2}{5}) = (\frac{2\times4}{5\times4}) = \frac{8}{20}$ $\newline$ $(\frac{3}{4}) = (\frac{3\times5}{4\times5}) = \frac{15}{20}$ $\newline$ Now we can subtract these fractions: $\newline$ $\frac{8}{20} - \frac{15}{20} = -\frac{7}{20}$ $\newline$ So the equation becomes: $\newline$ $-(\frac{2}{5})c = -\frac{7}{20}$
Solve for c: Solve for c by dividing both sides of the equation by $-\frac{2}{5}$ . $\newline$ To isolate c, we need to divide by $-\frac{2}{5}$ , which is the same as multiplying by the reciprocal, $-\frac{5}{2}$ . $\newline$ c = \left(-\frac{ $7$ }{ $20$ }\right) * \left(-\frac{ $5$ }{ $2$ }\right)
Multiply fractions: Multiply the fractions. $\newline$ When multiplying fractions, we multiply the numerators together and the denominators together: $\newline$ $c = \frac{-7 \times -5}{20 \times 2}$ $\newline$ $c = \frac{35}{40}$
Simplify fraction: Simplify the fraction. $\newline$ The fraction $\frac{35}{40}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $5$ . $\newline$ $c = \frac{35/5}{40/5}$ $\newline$ $c = \frac{7}{8}$