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

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

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

Rewrite.

$0 + 0 - \frac{5}{4} \cdot (3 x + 5) = \frac{1}{4} \cdot (- x + 1) - 3$

Simplify by adding zeros.

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

Apply the distributive property.

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

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

Multiply $3$ by $- 1$ .

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

Combine $- 3$ and $\frac{5}{4}$ .

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

Multiply $- 3$ by $5$ .

$\frac{- 15}{4} x - \frac{5}{4} \cdot 5 = \frac{1}{4} \cdot (- x + 1) - 3$

Combine $\frac{- 15}{4}$ and $x$ .

$\frac{- 15 x}{4} - \frac{5}{4} \cdot 5 = \frac{1}{4} \cdot (- x + 1) - 3$

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

Multiply $5$ by $- 1$ .

$\frac{- 15 x}{4} - 5 (\frac{5}{4}) = \frac{1}{4} \cdot (- x + 1) - 3$

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

$\frac{- 15 x}{4} + \frac{- 5 \cdot 5}{4} = \frac{1}{4} \cdot (- x + 1) - 3$

Multiply $- 5$ by $5$ .

$\frac{- 15 x}{4} + \frac{- 25}{4} = \frac{1}{4} \cdot (- x + 1) - 3$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{(15) x}{4} + \frac{- 25}{4} = \frac{1}{4} \cdot (- x + 1) - 3$

Move the negative in front of the fraction.

$- \frac{15 x}{4} - \frac{25}{4} = \frac{1}{4} \cdot (- x + 1) - 3$

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

Simplify each term.

Apply the distributive property.

$- \frac{15 x}{4} - \frac{25}{4} = \frac{1}{4} (- x) + \frac{1}{4} \cdot 1 - 3$

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

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} + \frac{1}{4} \cdot 1 - 3$

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

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} + \frac{1}{4} - 3$

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

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} + \frac{1}{4} - 3 \cdot \frac{4}{4}$

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

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} + \frac{1}{4} + \frac{- 3 \cdot 4}{4}$

Combine the numerators over the common denominator.

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} + \frac{1 - 3 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 3$ by $4$ .

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} + \frac{1 - 12}{4}$

Subtract $12$ from $1$ .

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} + \frac{- 11}{4}$

Move the negative in front of the fraction.

$- \frac{15 x}{4} - \frac{25}{4} = - \frac{x}{4} - \frac{11}{4}$

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

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

$- \frac{15 x}{4} - \frac{25}{4} + \frac{x}{4} = - \frac{11}{4}$

Combine the numerators over the common denominator.

$\frac{- 15 x - 25 + x}{4} = - \frac{11}{4}$

Add $- 15 x$ and $x$ .

$\frac{- 14 x - 25}{4} = - \frac{11}{4}$

Factor $- 1$ out of $- 14 x$ .

$\frac{- (14 x) - 25}{4} = - \frac{11}{4}$

Rewrite $- 25$ as $- 1 (25)$ .

$\frac{- (14 x) - 1 (25)}{4} = - \frac{11}{4}$

Factor $- 1$ out of $- (14 x) - 1 (25)$ .

$\frac{- (14 x + 25)}{4} = - \frac{11}{4}$

Rewrite $- (14 x + 25)$ as $- 1 (14 x + 25)$ .

$\frac{- 1 (14 x + 25)}{4} = - \frac{11}{4}$

Move the negative in front of the fraction.

$- \frac{14 x + 25}{4} = - \frac{11}{4}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- (14 x + 25) = - 11$

Simplify $- (14 x + 25)$ .

Apply the distributive property.

$- (14 x) - 1 \cdot 25 = - 11$

Multiply.

Multiply $14$ by $- 1$ .

$- 14 x - 1 \cdot 25 = - 11$

Multiply $- 1$ by $25$ .

$- 14 x - 25 = - 11$

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

Add $25$ to both sides of the equation.

$- 14 x = - 11 + 25$

Add $- 11$ and $25$ .

$- 14 x = 14$

Divide each term in $- 14 x = 14$ by $- 14$ and simplify.

Divide each term in $- 14 x = 14$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{14}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{14}{- 14}$

Divide $x$ by $1$ .

$x = \frac{14}{- 14}$

Simplify the right side.

Divide $14$ by $- 14$ .

$x = - 1$

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

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