Solve for X: Combining Fractions 1/4x - 1/5x + 2/3x - 2/5x = 1

To solve the given equation $\frac{1}{4}x - \frac{1}{5}x + \frac{2}{3}x - \frac{2}{5}x = 1$, follow these steps:

Step 1: Find a common denominator for the fractions involved. The denominators are 4, 5, 3, and again 5. The least common multiple (LCM) of these numbers is 60.

Step 2: Rewrite each fraction with the common denominator of 60:

• $\frac{1}{4}x = \frac{15}{60}x$
• $-\frac{1}{5}x = -\frac{12}{60}x$
• $\frac{2}{3}x = \frac{40}{60}x$
• $-\frac{2}{5}x = -\frac{24}{60}x$

Step 3: Combine the fractions:

$\frac{15}{60}x - \frac{12}{60}x + \frac{40}{60}x - \frac{24}{60}x$

This simplifies to:

$\frac{15 - 12 + 40 - 24}{60}x = \frac{19}{60}x$

Step 4: Set up the equation:

$\frac{19}{60}x = 1$

Step 5: Solve for $x$ by isolating it on one side of the equation. Multiply both sides by the reciprocal of $\frac{19}{60}$, which is $\frac{60}{19}$:

$x = 1 \times \frac{60}{19}$

$x = \frac{60}{19}$

Therefore, the solution to the problem is $x = \frac{60}{19} = \frac{15}{7}$ after simplifying the fraction.