Solve the Fraction Equation: Isolating X in (2-x)/(5*(3+x)-15) = 2/7

To solve this problem, we'll follow these steps:

• Step 1: Cross-multiply to eliminate the fraction.
• Step 2: Simplify both sides of the equation.
• Step 3: Solve for $x$.

Now, let's work through each step:

Step 1: Begin by cross-multiplying:

$(2-x) \times 7 = 2 \times (5 \times (3+x) - 15)$

This simplifies to:

$7(2-x) = 2(5(3+x) - 15)$

Step 2: Simplify both sides of the equation.
First, simplify the right-hand side:

$5(3+x) = 15 + 5x$

Then:

$5(3+x) - 15 = 15 + 5x - 15 = 5x$

So, the equation becomes:

$7(2-x) = 2(5x)$

Distribute and simplify both sides:

Left-hand side: $14 - 7x$

Right-hand side: $10x$

Thus, the equation is now:

$14 - 7x = 10x$

Step 3: Solve for $x$.
Rearrange to isolate $x$:

$14 = 10x + 7x$

$14 = 17x$

Divide both sides by 17 to solve for $x$:

$x = \frac{14}{17}$

Therefore, the solution to the problem is $x = \frac{14}{17}$.