Solve for x 14+5/7x-20=4(1/7x-1)

$14 + \frac{5}{7} x - 20 = 4 (\frac{1}{7} x - 1)$

Step 1

Simplify $14 + \frac{5}{7} x - 20$ .

Combine $\frac{5}{7}$ and $x$ .

$14 + \frac{5 x}{7} - 20 = 4 (\frac{1}{7} x - 1)$

Subtract $20$ from $14$ .

$\frac{5 x}{7} - 6 = 4 (\frac{1}{7} x - 1)$

Step 2

Simplify $4 (\frac{1}{7} x - 1)$ .

Combine $\frac{1}{7}$ and $x$ .

$\frac{5 x}{7} - 6 = 4 (\frac{x}{7} - 1)$

Apply the distributive property.

$\frac{5 x}{7} - 6 = 4 \frac{x}{7} + 4 \cdot - 1$

Combine $4$ and $\frac{x}{7}$ .

$\frac{5 x}{7} - 6 = \frac{4 x}{7} + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$\frac{5 x}{7} - 6 = \frac{4 x}{7} - 4$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{4 x}{7}$ from both sides of the equation.

$\frac{5 x}{7} - 6 - \frac{4 x}{7} = - 4$

Combine the numerators over the common denominator.

$- 6 + \frac{5 x - 4 x}{7} = - 4$

Subtract $4 x$ from $5 x$ .

$- 6 + \frac{x}{7} = - 4$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Add $6$ to both sides of the equation.

$\frac{x}{7} = - 4 + 6$

Add $- 4$ and $6$ .

$\frac{x}{7} = 2$

Step 5

Multiply both sides of the equation by $7$ .

$7 \frac{x}{7} = 7 \cdot 2$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{x}{7} = 7 \cdot 2$

Rewrite the expression.

$x = 7 \cdot 2$

Simplify the right side.

Multiply $7$ by $2$ .

$x = 14$