Solve for X in the Equation: 6/10 - 30x + 1/4 = 6/8 - 16x

To solve the equation $\frac{6}{10} - 30x + \frac{1}{4} = \frac{6}{8} - 16x$, follow these steps:

• Step 1: Simplify the fractions involved. We have $\frac{6}{10} = \frac{3}{5}$ and $\frac{6}{8} = \frac{3}{4}$.
• Step 2: The equation becomes $\frac{3}{5} - 30x + \frac{1}{4} = \frac{3}{4} - 16x$.
• Step 3: Combine the constant terms on each side. The left side is $\frac{3}{5} + \frac{1}{4}$. Find a common denominator, which is 20:
• $\frac{3}{5} = \frac{12}{20}$
• $\frac{1}{4} = \frac{5}{20}$
• So, $\frac{3}{5} + \frac{1}{4} = \frac{12}{20} + \frac{5}{20} = \frac{17}{20}$.
• Step 4: Substitute back into the equation: $\frac{17}{20} - 30x = \frac{3}{4} - 16x$.
• Step 5: Simplify the right side. $\frac{3}{4} = \frac{15}{20}$, so the equation becomes $\frac{17}{20} - 30x = \frac{15}{20} - 16x$.
• Step 6: Subtract $\frac{15}{20}$ from both sides to get $\frac{17}{20} - \frac{15}{20} - 30x = -16x$:
• $\frac{17}{20} - \frac{15}{20} = \frac{2}{20} = \frac{1}{10}$.
• So, the equation becomes $\frac{1}{10} - 30x = -16x$.
• Step 7: Rearrange the equation to solve for $x$ by adding $30x$ to both sides: $\frac{1}{10} = 30x - 16x$.
• Step 8: Simplify the equation: $\frac{1}{10} = 14x$.
• Step 9: Divide both sides by 14 to solve for $x$: $x = \frac{1}{10 \times 14} = \frac{1}{140}$.

Therefore, the solution to the problem is $x = \frac{1}{140}$.