Question

solve for the variable. $-\frac{2}{c}+\frac{2}{5}=\frac{3}{c}$\\$\bigcirc$ $c = \frac{20}{3}$\\$\bigcirc$ $c = \frac{15}{2}$\\$\bigcirc$ $c = \frac{25}{4}$\\$\bigcirc$ $c = \frac{25}{2}$

Explanation:

Step1: Isolate terms with $c$

Add $\frac{2}{c}$ to both sides:
$$\frac{2}{5} = \frac{3}{c} + \frac{2}{c}$$

Step2: Combine like fractions

Sum the right-hand side terms:
$$\frac{2}{5} = \frac{5}{c}$$

Step3: Cross-multiply to solve for $c$

Set products equal:
$$2c = 5 \times 5$$
$$2c = 25$$

Step4: Solve for $c$

Divide both sides by 2:
$$c = \frac{25}{2}$$

Answer:

$\boldsymbol{c=\frac{25}{2}}$