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

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

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

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

Simplify $2 (x - 1)$ .

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

$\frac{7 x}{4} - 5 = 2 x - 2$

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

Subtract $2 x$ from both sides of the equation.

$\frac{7 x}{4} - 5 - 2 x = - 2$

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 x}{4} - 2 x \cdot \frac{4}{4} - 5 = - 2$

Combine $- 2 x$ and $\frac{4}{4}$ .

$\frac{7 x}{4} + \frac{- 2 x \cdot 4}{4} - 5 = - 2$

Combine the numerators over the common denominator.

$\frac{7 x - 2 x \cdot 4}{4} - 5 = - 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $7 x - 2 x \cdot 4$ .

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 - 2 x \cdot 4}{4} - 5 = - 2$

Factor $x$ out of $- 2 x \cdot 4$ .

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

Factor $x$ out of $x \cdot 7 + x (- 2 \cdot 4)$ .

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

Multiply $- 2$ by $4$ .

$\frac{x (7 - 8)}{4} - 5 = - 2$

Subtract $8$ from $7$ .

$\frac{x \cdot - 1}{4} - 5 = - 2$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{4} - 5 = - 2$

Move the negative in front of the fraction.

$- \frac{x}{4} - 5 = - 2$

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

Add $5$ to both sides of the equation.

$- \frac{x}{4} = - 2 + 5$

Add $- 2$ and $5$ .

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

Multiply both sides of the equation by $- 4$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 4 \cdot 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 4 \cdot 3$

Multiply $x$ by $1$ .

$x = - 4 \cdot 3$

Simplify the right side.

Multiply $- 4$ by $3$ .

$x = - 12$

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

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