Solve the Linear Challenge: Simplify and Balance 38x + 2 - 3 = 19x - 7x + 2

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

• Simplify each fraction in the equation.
• Combine like terms involving $x$ on each side of the equation.
• Isolate the variable $x$ to solve the equation.

Now, let's work through each step:

Step 1: Simplify the fractions:

• $\frac{28}{14} = 2$
• $\frac{16}{8} = 2$
• The equation becomes:
  $38x + 2 - \frac{57}{19} = 19x - 7x + 2$

Step 2: Combine like terms and simplify the equation:

• Simplify the right side:
  $19x - 7x = 12x$
• The equation now is:
  $38x + 2 - \frac{57}{19} = 12x + 2$
• Eliminate the constant $2$ from both sides:
  $38x - \frac{57}{19} = 12x$

Step 3: Isolate the variable $x$:

• Subtract $12x$ from both sides:
  $38x - 12x - \frac{57}{19} = 0$
• The equation simplifies to:
  $26x - \frac{57}{19} = 0$
• Add $\frac{57}{19}$ to both sides:
  $26x = \frac{57}{19}$
• To isolate $x$, divide both sides by $26$:
  $x = \frac{57}{19 \times 26}$
• Calculate $19 \times 26 = 494$, so:
  $x = \frac{57}{494}$

Upon simplification, we find $x = \frac{3}{26}$.

Therefore, the solution to the problem is $x = \frac{3}{26}$.