Solve for X: Finding the Solution to (2/7)x - (2/3)x = 4

To solve the provided equation $\frac{2}{7}x - \frac{2}{3}x = 4$, we need to combine like terms on the left-hand side. Let's work step-by-step:

• Step 1: Identify the common denominator of the fractions $\frac{2}{7}$ and $\frac{2}{3}$.
  The least common denominator of 7 and 3 is 21.

• Step 2: Rewrite each term with the common denominator of 21:
  $\frac{2}{7}x = \frac{2 \times 3}{7 \times 3}x = \frac{6}{21}x$ and
  $\frac{2}{3}x = \frac{2 \times 7}{3 \times 7}x = \frac{14}{21}x$.

• Step 3: Combine these like terms:
  $\frac{6}{21}x - \frac{14}{21}x = \frac{6 - 14}{21}x = \frac{-8}{21}x$.

• Step 4: Rewrite the equation with the combined terms:
  $\frac{-8}{21}x = 4$.

• Step 5: Solve for $x$ by multiplying both sides by the reciprocal of $-\frac{8}{21}$:
  $x = 4 \times \frac{21}{-8} = 4 \times -\frac{21}{8} = -\frac{84}{8} = -10.5$ or $-10\frac{1}{2}$.

Therefore, the solution to the equation is $x = -10\frac{1}{2}$.