Solve for x -(-5/4x+3)-3x=-7(-1/4x+2)

$- (- \frac{5}{4} x + 3) - 3 x = - 7 (- \frac{1}{4} x + 2)$

Step 1

Simplify $- (- \frac{5}{4} x + 3) - 3 x$ .

Simplify each term.

Combine $x$ and $\frac{5}{4}$ .

$- (- \frac{x \cdot 5}{4} + 3) - 3 x = - 7 (- \frac{1}{4} x + 2)$

Move $5$ to the left of $x$ .

$- (- \frac{5 x}{4} + 3) - 3 x = - 7 (- \frac{1}{4} x + 2)$

Apply the distributive property.

$- - \frac{5 x}{4} - 1 \cdot 3 - 3 x = - 7 (- \frac{1}{4} x + 2)$

Multiply $- - \frac{5 x}{4}$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{5 x}{4} - 1 \cdot 3 - 3 x = - 7 (- \frac{1}{4} x + 2)$

Multiply $\frac{5 x}{4}$ by $1$ .

$\frac{5 x}{4} - 1 \cdot 3 - 3 x = - 7 (- \frac{1}{4} x + 2)$

Multiply $- 1$ by $3$ .

$\frac{5 x}{4} - 3 - 3 x = - 7 (- \frac{1}{4} x + 2)$

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x}{4} - 3 x \cdot \frac{4}{4} - 3 = - 7 (- \frac{1}{4} x + 2)$

Simplify terms.

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

$\frac{5 x}{4} + \frac{- 3 x \cdot 4}{4} - 3 = - 7 (- \frac{1}{4} x + 2)$

Combine the numerators over the common denominator.

$\frac{5 x - 3 x \cdot 4}{4} - 3 = - 7 (- \frac{1}{4} x + 2)$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - 3 x \cdot 4$ .

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - 3 x \cdot 4}{4} - 3 = - 7 (- \frac{1}{4} x + 2)$

Factor $x$ out of $- 3 x \cdot 4$ .

$\frac{x \cdot 5 + x (- 3 \cdot 4)}{4} - 3 = - 7 (- \frac{1}{4} x + 2)$

Factor $x$ out of $x \cdot 5 + x (- 3 \cdot 4)$ .

$\frac{x (5 - 3 \cdot 4)}{4} - 3 = - 7 (- \frac{1}{4} x + 2)$

Multiply $- 3$ by $4$ .

$\frac{x (5 - 12)}{4} - 3 = - 7 (- \frac{1}{4} x + 2)$

Subtract $12$ from $5$ .

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

Move $- 7$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Step 2

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

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

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

Apply the distributive property.

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

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

Multiply $- 1$ by $- 7$ .

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

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

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

Multiply $- 7$ by $2$ .

$- \frac{7 x}{4} - 3 = \frac{7 x}{4} - 14$

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.

$- \frac{7 x}{4} - 3 - \frac{7 x}{4} = - 14$

Combine the numerators over the common denominator.

$- 3 + \frac{- 7 x - 7 x}{4} = - 14$

Subtract $7 x$ from $- 7 x$ .

$- 3 + \frac{- 14 x}{4} = - 14$

Simplify each term.

Cancel the common factor of $- 14$ and $4$ .

Factor $2$ out of $- 14 x$ .

$- 3 + \frac{2 (- 7 x)}{4} = - 14$

Cancel the common factors.

Factor $2$ out of $4$ .

$- 3 + \frac{2 (- 7 x)}{2 (2)} = - 14$

Cancel the common factor.

$- 3 + \frac{2 (- 7 x)}{2 \cdot 2} = - 14$

Rewrite the expression.

$- 3 + \frac{- 7 x}{2} = - 14$

Move the negative in front of the fraction.

$- 3 - \frac{7 x}{2} = - 14$

Step 4

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

Add $3$ to both sides of the equation.

$- \frac{7 x}{2} = - 14 + 3$

Add $- 14$ and $3$ .

$- \frac{7 x}{2} = - 11$

Step 5

Multiply both sides of the equation by $- \frac{2}{7}$ .

$- \frac{2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot - 11$

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{- 2}{7} (- \frac{7 x}{2}) = - \frac{2}{7} \cdot - 11$

Move the leading negative in $- \frac{7 x}{2}$ into the numerator.

$\frac{- 2}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 11$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 11$

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- 7 x}{2} = - \frac{2}{7} \cdot - 11$

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{2}{7} \cdot - 11$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot - 11$

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{2}{7} \cdot - 11$

Rewrite the expression.

$- - x = - \frac{2}{7} \cdot - 11$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{7} \cdot - 11$

Multiply $x$ by $1$ .

$x = - \frac{2}{7} \cdot - 11$

Simplify the right side.

Multiply $- \frac{2}{7} \cdot - 11$ .

Multiply $- 11$ by $- 1$ .

$x = 11 (\frac{2}{7})$

Combine $11$ and $\frac{2}{7}$ .

$x = \frac{11 \cdot 2}{7}$

Multiply $11$ by $2$ .

$x = \frac{22}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{22}{7}$

Decimal Form:

$x = 3.\overline{142857}$

Mixed Number Form:

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

Solve for x -(-5/4x+3)-3x=-7(-1/4x+2)

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