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

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

Step 1

Simplify $- (- 2 x + 7) - x$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 2$ by $- 1$ .

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

Multiply $- 1$ by $7$ .

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

Subtract $x$ from $2 x$ .

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

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

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

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

Factor $x$ out of $3 x$ .

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

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

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

Multiply $- 2$ by $2$ .

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

Add $- 4$ and $3$ .

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

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

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

Move the negative in front of the fraction.

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

Step 3

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

Add $\frac{x}{2}$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $x \cdot 2$ and $x$ .

Reorder $x$ and $2$ .

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

Add $2 \cdot x$ and $x$ .

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

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

Step 4

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

Add $7$ to both sides of the equation.

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

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $7$ by $4$ .

$\frac{3 x}{2} = \frac{- 3 + 28}{4}$

Add $- 3$ and $28$ .

$\frac{3 x}{2} = \frac{25}{4}$

Step 5

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot \frac{25}{4}$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot \frac{25}{4}$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{25}{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot \frac{25}{4}$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{25}{4}$

Rewrite the expression.

$x = \frac{2}{3} \cdot \frac{25}{4}$

Simplify the right side.

Simplify $\frac{2}{3} \cdot \frac{25}{4}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{2}{3} \cdot \frac{25}{2 (2)}$

Cancel the common factor.

$x = \frac{2}{3} \cdot \frac{25}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{25}{2}$

Multiply $\frac{1}{3}$ by $\frac{25}{2}$ .

$x = \frac{25}{3 \cdot 2}$

Multiply $3$ by $2$ .

$x = \frac{25}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{6}$

Decimal Form:

$x = 4.1\overline{6}$

Mixed Number Form:

$x = 4 \frac{1}{6}$

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

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