Fraction Equation Challenge: Solve 7x + 6/8 - 2/4 = 12/2x + 1/8

To solve this equation, we will proceed with the following steps:

• Simplify the fractions and expressions on both sides of the equation.
• Combine and move like terms to isolate the variable $x$.
• Solve for $x$.

Let's begin by simplifying both sides of the equation:

The original equation is: $7x + \frac{6}{8} - \frac{2}{4} = \frac{12}{2}x + \frac{1}{8}$.

First, simplify the fractions:

• $\frac{6}{8}$ simplifies to $\frac{3}{4}$.
• $\frac{2}{4}$ simplifies to $\frac{1}{2}$.
• $\frac{12}{2}$ simplifies to $6$.

The equation becomes: $7x + \frac{3}{4} - \frac{1}{2} = 6x + \frac{1}{8}$.

Next, simplify by combining terms where possible: - On the left side, the constant terms are $\frac{3}{4} - \frac{1}{2}$. - Convert $\frac{1}{2}$ to $\frac{2}{4}$ to subtract easily: $\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$. Thus, the equation becomes: $7x + \frac{1}{4} = 6x + \frac{1}{8}$.

Now, move all terms involving $x$ to one side and constants to the other:

• Subtract $6x$ from both sides: $7x - 6x + \frac{1}{4} = \frac{1}{8}$, which simplifies to $x + \frac{1}{4} = \frac{1}{8}$.
• Next, subtract $\frac{1}{4}$ from both sides to isolate $x$: $x = \frac{1}{8} - \frac{1}{4}$
• Convert $\frac{1}{4}$ to $\frac{2}{8}$ to subtract: $x = \frac{1}{8} - \frac{2}{8} = -\frac{1}{8}$

Therefore, the value of $x$ that solves the equation is $x = -\frac{1}{8}$.