Solve for x 1/4x-1/7(2x-4)=1

$\frac{1}{4} x - \frac{1}{7} (2 x - 4) = 1$

Step 1

Simplify $\frac{1}{4} x - \frac{1}{7} \cdot (2 x - 4)$ .

Simplify each term.

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - \frac{1}{7} \cdot (2 x - 4) = 1$

Apply the distributive property.

$\frac{x}{4} - \frac{1}{7} (2 x) - \frac{1}{7} \cdot - 4 = 1$

Multiply $- \frac{1}{7} (2 x)$ .

Multiply $2$ by $- 1$ .

$\frac{x}{4} - 2 (\frac{1}{7}) x - \frac{1}{7} \cdot - 4 = 1$

Combine $- 2$ and $\frac{1}{7}$ .

$\frac{x}{4} + \frac{- 2}{7} x - \frac{1}{7} \cdot - 4 = 1$

Combine $\frac{- 2}{7}$ and $x$ .

$\frac{x}{4} + \frac{- 2 x}{7} - \frac{1}{7} \cdot - 4 = 1$

Multiply $- \frac{1}{7} \cdot - 4$ .

Multiply $- 4$ by $- 1$ .

$\frac{x}{4} + \frac{- 2 x}{7} + 4 (\frac{1}{7}) = 1$

Combine $4$ and $\frac{1}{7}$ .

$\frac{x}{4} + \frac{- 2 x}{7} + \frac{4}{7} = 1$

Move the negative in front of the fraction.

$\frac{x}{4} - \frac{2 x}{7} + \frac{4}{7} = 1$

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{x}{4} \cdot \frac{7}{7} - \frac{2 x}{7} + \frac{4}{7} = 1$

To write $- \frac{2 x}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} \cdot \frac{7}{7} - \frac{2 x}{7} \cdot \frac{4}{4} + \frac{4}{7} = 1$

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{4}$ by $\frac{7}{7}$ .

$\frac{x \cdot 7}{4 \cdot 7} - \frac{2 x}{7} \cdot \frac{4}{4} + \frac{4}{7} = 1$

Multiply $4$ by $7$ .

$\frac{x \cdot 7}{28} - \frac{2 x}{7} \cdot \frac{4}{4} + \frac{4}{7} = 1$

Multiply $\frac{2 x}{7}$ by $\frac{4}{4}$ .

$\frac{x \cdot 7}{28} - \frac{2 x \cdot 4}{7 \cdot 4} + \frac{4}{7} = 1$

Multiply $7$ by $4$ .

$\frac{x \cdot 7}{28} - \frac{2 x \cdot 4}{28} + \frac{4}{7} = 1$

Combine the numerators over the common denominator.

$\frac{x \cdot 7 - 2 x \cdot 4}{28} + \frac{4}{7} = 1$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 7 - 2 x \cdot 4$ .

Factor $x$ out of $x \cdot 7$ .

$\frac{x (7) - 2 x \cdot 4}{28} + \frac{4}{7} = 1$

Factor $x$ out of $- 2 x \cdot 4$ .

$\frac{x (7) + x (- 2 \cdot 4)}{28} + \frac{4}{7} = 1$

Factor $x$ out of $x (7) + x (- 2 \cdot 4)$ .

$\frac{x (7 - 2 \cdot 4)}{28} + \frac{4}{7} = 1$

Multiply $- 2$ by $4$ .

$\frac{x (7 - 8)}{28} + \frac{4}{7} = 1$

Subtract $8$ from $7$ .

$\frac{x \cdot - 1}{28} + \frac{4}{7} = 1$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{28} + \frac{4}{7} = 1$

Move the negative in front of the fraction.

$- \frac{x}{28} + \frac{4}{7} = 1$

Step 2

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

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

$- \frac{x}{28} = 1 - \frac{4}{7}$

Write $1$ as a fraction with a common denominator.

$- \frac{x}{28} = \frac{7}{7} - \frac{4}{7}$

Combine the numerators over the common denominator.

$- \frac{x}{28} = \frac{7 - 4}{7}$

Subtract $4$ from $7$ .

$- \frac{x}{28} = \frac{3}{7}$

Step 3

Multiply both sides of the equation by $- 28$ .

$- 28 (- \frac{x}{28}) = - 28 (\frac{3}{7})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 28 (- \frac{x}{28})$ .

Cancel the common factor of $28$ .

Move the leading negative in $- \frac{x}{28}$ into the numerator.

$- 28 \frac{- x}{28} = - 28 (\frac{3}{7})$

Factor $28$ out of $- 28$ .

$28 (- 1) \frac{- x}{28} = - 28 (\frac{3}{7})$

Cancel the common factor.

$28 \cdot - 1 \frac{- x}{28} = - 28 (\frac{3}{7})$

Rewrite the expression.

$- - x = - 28 (\frac{3}{7})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 28 (\frac{3}{7})$

Multiply $x$ by $1$ .

$x = - 28 (\frac{3}{7})$

Simplify the right side.

Simplify $- 28 (\frac{3}{7})$ .

Cancel the common factor of $7$ .

Factor $7$ out of $- 28$ .

$x = 7 (- 4) \frac{3}{7}$

Cancel the common factor.

$x = 7 \cdot - 4 \frac{3}{7}$

Rewrite the expression.

$x = - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$x = - 12$

Solve for x 1/4x-1/7(2x-4)=1

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