Solve for x -4/7(x-1/4)=3/7

$- \frac{4}{7} (x - \frac{1}{4}) = \frac{3}{7}$

Multiply both sides of the equation by $- \frac{7}{4}$ .

$- \frac{7}{4} (- \frac{4}{7} \cdot (x - \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

Simplify both sides of the equation.

Simplify the left side.

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

Simplify terms.

Apply the distributive property.

$- \frac{7}{4} (- \frac{4}{7} x - \frac{4}{7} (- \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

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

$- \frac{7}{4} (- \frac{x \cdot 4}{7} - \frac{4}{7} (- \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- 4}{7} (- \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- 4}{7} \cdot \frac{- 1}{4}) = - \frac{7}{4} \cdot \frac{3}{7}$

Factor $4$ out of $- 4$ .

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{4 (- 1)}{7} \cdot \frac{- 1}{4}) = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{4 \cdot - 1}{7} \cdot \frac{- 1}{4}) = - \frac{7}{4} \cdot \frac{3}{7}$

Rewrite the expression.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- 1}{7} \cdot - 1) = - \frac{7}{4} \cdot \frac{3}{7}$

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

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- - 1}{7}) = - \frac{7}{4} \cdot \frac{3}{7}$

Multiply $- 1$ by $- 1$ .

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{1}{7}) = - \frac{7}{4} \cdot \frac{3}{7}$

Move $4$ to the left of $x$ .

$- \frac{7}{4} (- \frac{4 x}{7} + \frac{1}{7}) = - \frac{7}{4} \cdot \frac{3}{7}$

Simplify terms.

Apply the distributive property.

$- \frac{7}{4} (- \frac{4 x}{7}) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$\frac{- 7}{4} (- \frac{4 x}{7}) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Move the leading negative in $- \frac{4 x}{7}$ into the numerator.

$\frac{- 7}{4} \cdot \frac{- 4 x}{7} - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{4} \cdot \frac{- 4 x}{7} - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor.

$\frac{7 \cdot - 1}{4} \cdot \frac{- 4 x}{7} - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Rewrite the expression.

$\frac{- 1}{4} (- 4 x) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 x$ .

$\frac{- 1}{4} (4 (- x)) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor.

$\frac{- 1}{4} (4 (- x)) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Rewrite the expression.

$- - x - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Multiply $x$ by $1$ .

$x - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$x + \frac{- 7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Factor $7$ out of $- 7$ .

$x + \frac{7 (- 1)}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Cancel the common factor.

$x + \frac{7 \cdot - 1}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Rewrite the expression.

$x + \frac{- 1}{4} = - \frac{7}{4} \cdot \frac{3}{7}$

Move the negative in front of the fraction.

$x - \frac{1}{4} = - \frac{7}{4} \cdot \frac{3}{7}$

Simplify the right side.

Simplify $- \frac{7}{4} \cdot \frac{3}{7}$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$x - \frac{1}{4} = \frac{- 7}{4} \cdot \frac{3}{7}$

Factor $7$ out of $- 7$ .

$x - \frac{1}{4} = \frac{7 (- 1)}{4} \cdot \frac{3}{7}$

Cancel the common factor.

$x - \frac{1}{4} = \frac{7 \cdot - 1}{4} \cdot \frac{3}{7}$

Rewrite the expression.

$x - \frac{1}{4} = \frac{- 1}{4} \cdot 3$

Combine $\frac{- 1}{4}$ and $3$ .

$x - \frac{1}{4} = \frac{- 1 \cdot 3}{4}$

Simplify the expression.

Multiply $- 1$ by $3$ .

$x - \frac{1}{4} = \frac{- 3}{4}$

Move the negative in front of the fraction.

$x - \frac{1}{4} = - \frac{3}{4}$

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

Add $\frac{1}{4}$ to both sides of the equation.

$x = - \frac{3}{4} + \frac{1}{4}$

Combine the numerators over the common denominator.

$x = \frac{- 3 + 1}{4}$

Add $- 3$ and $1$ .

$x = \frac{- 2}{4}$

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{- 1}{2}$

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$

Solve for x -4/7(x-1/4)=3/7

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