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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Combine the numerators over the common denominator.

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

Subtract $7 x$ from $- x$ .

$- 4 + \frac{- 8 x}{4} = - 3$

Cancel the common factor of $- 8$ and $4$ .

Factor $4$ out of $- 8 x$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- 2 x$ by $1$ .

$- 4 - 2 x = - 3$

Step 4

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

Add $4$ to both sides of the equation.

$- 2 x = - 3 + 4$

Add $- 3$ and $4$ .

$- 2 x = 1$

Step 5

Divide each term in $- 2 x = 1$ by $- 2$ and simplify.

Divide each term in $- 2 x = 1$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$

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

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