Solve for x -3/2x-(-x-1)=-6x+2(4x-1/4)

$- \frac{3}{2} x - (- x - 1) = - 6 x + 2 (4 x - \frac{1}{4})$

Step 1

Simplify $- \frac{3}{2} x - (- x - 1)$ .

Simplify each term.

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

$- \frac{x \cdot 3}{2} - (- x - 1) = - 6 x + 2 (4 x - \frac{1}{4})$

Move $3$ to the left of $x$ .

$- \frac{3 \cdot x}{2} - (- x - 1) = - 6 x + 2 (4 x - \frac{1}{4})$

Apply the distributive property.

$- \frac{3 x}{2} - - x - - 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$- \frac{3 x}{2} + 1 x - - 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Multiply $x$ by $1$ .

$- \frac{3 x}{2} + x - - 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Multiply $- 1$ by $- 1$ .

$- \frac{3 x}{2} + x + 1 = - 6 x + 2 (4 x - \frac{1}{4})$

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

$- \frac{3 x}{2} + x \cdot \frac{2}{2} + 1 = - 6 x + 2 (4 x - \frac{1}{4})$

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

$- \frac{3 x}{2} + \frac{x \cdot 2}{2} + 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Combine the numerators over the common denominator.

$\frac{- 3 x + x \cdot 2}{2} + 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Add $- 3 x$ and $x \cdot 2$ .

Reorder $x$ and $2$ .

$\frac{- 3 x + 2 \cdot x}{2} + 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Add $- 3 x$ and $2 \cdot x$ .

$\frac{- x}{2} + 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Move the negative in front of the fraction.

$- \frac{x}{2} + 1 = - 6 x + 2 (4 x - \frac{1}{4})$

Step 2

Simplify $- 6 x + 2 (4 x - \frac{1}{4})$ .

Simplify each term.

Apply the distributive property.

$- \frac{x}{2} + 1 = - 6 x + 2 (4 x) + 2 (- \frac{1}{4})$

Multiply $4$ by $2$ .

$- \frac{x}{2} + 1 = - 6 x + 8 x + 2 (- \frac{1}{4})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- \frac{x}{2} + 1 = - 6 x + 8 x + 2 (\frac{- 1}{4})$

Factor $2$ out of $4$ .

$- \frac{x}{2} + 1 = - 6 x + 8 x + 2 \frac{- 1}{2 (2)}$

Cancel the common factor.

$- \frac{x}{2} + 1 = - 6 x + 8 x + 2 \frac{- 1}{2 \cdot 2}$

Rewrite the expression.

$- \frac{x}{2} + 1 = - 6 x + 8 x + \frac{- 1}{2}$

Move the negative in front of the fraction.

$- \frac{x}{2} + 1 = - 6 x + 8 x - \frac{1}{2}$

Add $- 6 x$ and $8 x$ .

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

Step 3

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $- x$ .

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

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

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

Factor $x$ out of $x \cdot - 1 + x (- 2 \cdot 2)$ .

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

Multiply $- 2$ by $2$ .

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

Subtract $4$ from $- 1$ .

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

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

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

Move the negative in front of the fraction.

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

Step 4

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

Subtract $1$ from both sides of the equation.

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

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 1$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $- 1$ .

$- \frac{5 x}{2} = \frac{- 3}{2}$

Move the negative in front of the fraction.

$- \frac{5 x}{2} = - \frac{3}{2}$

Step 5

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

$- 5 x = - 3$

Step 6

Divide each term in $- 5 x = - 3$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 3$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 3}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 3}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{3}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{5}$

Decimal Form:

$x = 0.6$

Solve for x -3/2x-(-x-1)=-6x+2(4x-1/4)

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