Solve the Fraction Equation: Finding X in (1/8)(x-3) + 5x = 1

To solve the given equation, $\frac{1}{8}(x - 3) + 5x = 1$, we will proceed with the following steps:

• Step 1: Distribute $\frac{1}{8}$ across the terms inside the parenthesis.

• Step 2: Combine like terms to simplify the equation.

• Step 3: Isolate the variable $x$ to find its value.

Now, let's work through each step:
Step 1: Distribute $\frac{1}{8}$ into the terms inside the parentheses:

$\frac{1}{8} \cdot x - \frac{1}{8} \cdot 3 = \frac{x}{8} - \frac{3}{8}$

So the equation becomes:

$\frac{x}{8} - \frac{3}{8} + 5x = 1$

Step 2: Combine like terms. First, combine the terms with $x$:

$5x + \frac{x}{8} = \frac{40x}{8} + \frac{x}{8} = \frac{41x}{8}$

Substitute back into the equation:

$\frac{41x}{8} - \frac{3}{8} = 1$

Step 3: Isolate $x$: add $\frac{3}{8}$ to both sides:

$\frac{41x}{8} = 1 + \frac{3}{8}$$\frac{41x}{8} = \frac{8}{8} + \frac{3}{8} = \frac{11}{8}$

Multiply both sides by 8 to eliminate the fraction:

$41x = 11$

Finally, divide both sides by 41 to solve for $x$:

$x=\frac{11}{41}$