Solve for X: Finding the Value in (2/4 + 1/2 + 3/8 - 1/5)x = 1

To solve this equation, we will follow these steps:

• Step 1: Identify the least common denominator (LCD) for the fractions $\frac{2}{4}x$, $\frac{1}{2}x$, $\frac{3}{8}x$, and $\frac{1}{5}x$.
• Step 2: Convert each fraction to have the LCD as the denominator.
• Step 3: Combine the fractions to form a single expression.
• Step 4: Solve the resulting equation for $x$.

Now, let's work through each step:

Step 1: The denominators are 4, 2, 8, and 5. The LCD of these numbers is 40.

Step 2: Convert each fraction:

$\frac{2}{4}x = \frac{2 \times 10}{40}x = \frac{20}{40}x$

$\frac{1}{2}x = \frac{1 \times 20}{40}x = \frac{20}{40}x$

$\frac{3}{8}x = \frac{3 \times 5}{40}x = \frac{15}{40}x$

$-\frac{1}{5}x = -\frac{1 \times 8}{40}x = -\frac{8}{40}x$

Step 3: Combine all fractions:

$\frac{20}{40}x + \frac{20}{40}x + \frac{15}{40}x - \frac{8}{40}x$

$= \frac{20 + 20 + 15 - 8}{40}x$

$= \frac{47}{40}x$

Step 4: Solve the equation $\frac{47}{40}x = 1$.

Multiply both sides by $\frac{40}{47}$ to solve for $x$:

$x = 1 \times \frac{40}{47}$

$x = \frac{40}{47}$

Therefore, the solution to the problem is $x = \frac{40}{47}$.