Solve for x -3/4(2x+1)+4=1/4-7x

$- \frac{3}{4} (2 x + 1) + 4 = \frac{1}{4} - 7 x$

Simplify $- \frac{3}{4} \cdot (2 x + 1) + 4$ .

Simplify each term.

Apply the distributive property.

$- \frac{3}{4} (2 x) - \frac{3}{4} \cdot 1 + 4 = \frac{1}{4} - 7 x$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (2 x) - \frac{3}{4} \cdot 1 + 4 = \frac{1}{4} - 7 x$

Factor $2$ out of $4$ .

$\frac{- 3}{2 (2)} (2 x) - \frac{3}{4} \cdot 1 + 4 = \frac{1}{4} - 7 x$

Factor $2$ out of $2 x$ .

$\frac{- 3}{2 (2)} (2 (x)) - \frac{3}{4} \cdot 1 + 4 = \frac{1}{4} - 7 x$

Cancel the common factor.

$\frac{- 3}{2 \cdot 2} (2 x) - \frac{3}{4} \cdot 1 + 4 = \frac{1}{4} - 7 x$

Rewrite the expression.

$\frac{- 3}{2} x - \frac{3}{4} \cdot 1 + 4 = \frac{1}{4} - 7 x$

Combine $\frac{- 3}{2}$ and $x$ .

$\frac{- 3 x}{2} - \frac{3}{4} \cdot 1 + 4 = \frac{1}{4} - 7 x$

Multiply $- 1$ by $1$ .

$\frac{- 3 x}{2} - \frac{3}{4} + 4 = \frac{1}{4} - 7 x$

Move the negative in front of the fraction.

$- \frac{3 x}{2} - \frac{3}{4} + 4 = \frac{1}{4} - 7 x$

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

$- \frac{3 x}{2} - \frac{3}{4} + 4 \cdot \frac{4}{4} = \frac{1}{4} - 7 x$

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

$- \frac{3 x}{2} - \frac{3}{4} + \frac{4 \cdot 4}{4} = \frac{1}{4} - 7 x$

Combine the numerators over the common denominator.

$- \frac{3 x}{2} + \frac{- 3 + 4 \cdot 4}{4} = \frac{1}{4} - 7 x$

Simplify the numerator.

Multiply $4$ by $4$ .

$- \frac{3 x}{2} + \frac{- 3 + 16}{4} = \frac{1}{4} - 7 x$

Add $- 3$ and $16$ .

$- \frac{3 x}{2} + \frac{13}{4} = \frac{1}{4} - 7 x$

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

Add $7 x$ to both sides of the equation.

$- \frac{3 x}{2} + \frac{13}{4} + 7 x = \frac{1}{4}$

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

$- \frac{3 x}{2} + 7 x \cdot \frac{2}{2} + \frac{13}{4} = \frac{1}{4}$

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

$- \frac{3 x}{2} + \frac{7 x \cdot 2}{2} + \frac{13}{4} = \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{- 3 x + 7 x \cdot 2}{2} + \frac{13}{4} = \frac{1}{4}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 3 x + 7 x \cdot 2$ .

Factor $x$ out of $- 3 x$ .

$\frac{x \cdot - 3 + 7 x \cdot 2}{2} + \frac{13}{4} = \frac{1}{4}$

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

$\frac{x \cdot - 3 + x (7 \cdot 2)}{2} + \frac{13}{4} = \frac{1}{4}$

Factor $x$ out of $x \cdot - 3 + x (7 \cdot 2)$ .

$\frac{x (- 3 + 7 \cdot 2)}{2} + \frac{13}{4} = \frac{1}{4}$

Multiply $7$ by $2$ .

$\frac{x (- 3 + 14)}{2} + \frac{13}{4} = \frac{1}{4}$

Add $- 3$ and $14$ .

$\frac{x \cdot 11}{2} + \frac{13}{4} = \frac{1}{4}$

Move $11$ to the left of $x$ .

$\frac{11 x}{2} + \frac{13}{4} = \frac{1}{4}$

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

Subtract $\frac{13}{4}$ from both sides of the equation.

$\frac{11 x}{2} = \frac{1}{4} - \frac{13}{4}$

Combine the numerators over the common denominator.

$\frac{11 x}{2} = \frac{1 - 13}{4}$

Subtract $13$ from $1$ .

$\frac{11 x}{2} = \frac{- 12}{4}$

Divide $- 12$ by $4$ .

$\frac{11 x}{2} = - 3$

Multiply both sides of the equation by $\frac{2}{11}$ .

$\frac{2}{11} \cdot \frac{11 x}{2} = \frac{2}{11} \cdot - 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{11} \cdot \frac{11 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{11} \cdot \frac{11 x}{2} = \frac{2}{11} \cdot - 3$

Rewrite the expression.

$\frac{1}{11} (11 x) = \frac{2}{11} \cdot - 3$

Cancel the common factor of $11$ .

Factor $11$ out of $11 x$ .

$\frac{1}{11} (11 (x)) = \frac{2}{11} \cdot - 3$

Cancel the common factor.

$\frac{1}{11} (11 x) = \frac{2}{11} \cdot - 3$

Rewrite the expression.

$x = \frac{2}{11} \cdot - 3$

Simplify the right side.

Simplify $\frac{2}{11} \cdot - 3$ .

Multiply $\frac{2}{11} \cdot - 3$ .

Combine $\frac{2}{11}$ and $- 3$ .

$x = \frac{2 \cdot - 3}{11}$

Multiply $2$ by $- 3$ .

$x = \frac{- 6}{11}$

Move the negative in front of the fraction.

$x = - \frac{6}{11}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{6}{11}$

Decimal Form:

$x = - 0.\overline{54}$

Solve for x -3/4(2x+1)+4=1/4-7x

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