Question

simplify the equation: 3/5(5x - 1/4) = 2/5

Explanation:

Step1: Eliminate fraction coefficient

Multiply both sides by $\frac{5}{3}$ to get rid of $\frac{3}{5}$ on the left:
$\frac{5}{3} \times \frac{3}{5}(5x - \frac{1}{4}) = \frac{2}{5} \times \frac{5}{3}$
Simplify: $5x - \frac{1}{4} = \frac{2}{3}$

Step2: Isolate the term with x

Add $\frac{1}{4}$ to both sides:
$5x = \frac{2}{3} + \frac{1}{4}$

Step3: Find common denominator and add

Common denominator of 3 and 4 is 12:
$5x = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Step4: Solve for x

Divide both sides by 5:
$x = \frac{11}{12} \div 5 = \frac{11}{12} \times \frac{1}{5} = \frac{11}{60}$

Answer:

$\frac{11}{60}$