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

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

• Step 1: Find a common denominator to combine the fractions on the left-hand side.
• Step 2: Simplify the equation.
• Step 3: Isolate the variable $x$.

Now, let's work through each step:
Step 1: The denominators are 5 and 4. The least common denominator (LCD) is 20.
Convert each term: $\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$ and $\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$.

Step 2: Combine the fractions: $\frac{8}{20}x + \frac{15}{20}x = \frac{23}{20}x$.
The equation now is $\frac{23}{20}x = 1$.

Step 3: Solve for $x$ by multiplying both sides by the reciprocal of $\frac{23}{20}$, which is $\frac{20}{23}$.
Thus, $x = 1 \times \frac{20}{23} = \frac{20}{23}$.

Therefore, the solution to the equation is $\boxed{\frac{20}{23}}$.