Solve for x 1/2-(7x-4)=-1/2(-x-6)

$\frac{1}{2} - (7 x - 4) = - \frac{1}{2} (- x - 6)$

Step 1

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

Simplify each term.

Apply the distributive property.

$\frac{1}{2} - (7 x) - - 4 = - \frac{1}{2} \cdot (- x - 6)$

Multiply $7$ by $- 1$ .

$\frac{1}{2} - 7 x - - 4 = - \frac{1}{2} \cdot (- x - 6)$

Multiply $- 1$ by $- 4$ .

$\frac{1}{2} - 7 x + 4 = - \frac{1}{2} \cdot (- x - 6)$

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

$- 7 x + \frac{1}{2} + 4 \cdot \frac{2}{2} = - \frac{1}{2} \cdot (- x - 6)$

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

$- 7 x + \frac{1}{2} + \frac{4 \cdot 2}{2} = - \frac{1}{2} \cdot (- x - 6)$

Combine the numerators over the common denominator.

$- 7 x + \frac{1 + 4 \cdot 2}{2} = - \frac{1}{2} \cdot (- x - 6)$

Simplify the numerator.

Multiply $4$ by $2$ .

$- 7 x + \frac{1 + 8}{2} = - \frac{1}{2} \cdot (- x - 6)$

Add $1$ and $8$ .

$- 7 x + \frac{9}{2} = - \frac{1}{2} \cdot (- x - 6)$

Step 2

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

Apply the distributive property.

$- 7 x + \frac{9}{2} = - \frac{1}{2} (- x) - \frac{1}{2} \cdot - 6$

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

Multiply $- 1$ by $- 1$ .

$- 7 x + \frac{9}{2} = 1 (\frac{1}{2}) x - \frac{1}{2} \cdot - 6$

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

$- 7 x + \frac{9}{2} = \frac{1}{2} x - \frac{1}{2} \cdot - 6$

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

$- 7 x + \frac{9}{2} = \frac{x}{2} - \frac{1}{2} \cdot - 6$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 7 x + \frac{9}{2} = \frac{x}{2} + \frac{- 1}{2} \cdot - 6$

Factor $2$ out of $- 6$ .

$- 7 x + \frac{9}{2} = \frac{x}{2} + \frac{- 1}{2} \cdot (2 (- 3))$

Cancel the common factor.

$- 7 x + \frac{9}{2} = \frac{x}{2} + \frac{- 1}{2} \cdot (2 \cdot - 3)$

Rewrite the expression.

$- 7 x + \frac{9}{2} = \frac{x}{2} - 1 \cdot - 3$

Multiply $- 1$ by $- 3$ .

$- 7 x + \frac{9}{2} = \frac{x}{2} + 3$

Step 3

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

Subtract $\frac{x}{2}$ from both sides of the equation.

$- 7 x + \frac{9}{2} - \frac{x}{2} = 3$

To write $- 7 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 7 x \cdot \frac{2}{2} - \frac{x}{2} + \frac{9}{2} = 3$

Combine $- 7 x$ and $\frac{2}{2}$ .

$\frac{- 7 x \cdot 2}{2} - \frac{x}{2} + \frac{9}{2} = 3$

Combine the numerators over the common denominator.

$\frac{- 7 x \cdot 2 - x}{2} + \frac{9}{2} = 3$

Combine the numerators over the common denominator.

$\frac{- 7 x \cdot 2 - x + 9}{2} = 3$

Multiply $2$ by $- 7$ .

$\frac{- 14 x - x + 9}{2} = 3$

Subtract $x$ from $- 14 x$ .

$\frac{- 15 x + 9}{2} = 3$

Factor $3$ out of $- 15 x + 9$ .

Factor $3$ out of $- 15 x$ .

$\frac{3 (- 5 x) + 9}{2} = 3$

Factor $3$ out of $9$ .

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

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

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

Factor $- 1$ out of $- 5 x$ .

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

Rewrite $3$ as $- 1 (- 3)$ .

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

Factor $- 1$ out of $- (5 x) - 1 (- 3)$ .

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

Rewrite $- (5 x - 3)$ as $- 1 (5 x - 3)$ .

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

Move the negative in front of the fraction.

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

Step 4

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

$- \frac{2}{3} (- \frac{3 (5 x - 3)}{2}) = - \frac{2}{3} \cdot 3$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{3} (- \frac{3 (5 x - 3)}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 (5 x - 3)}{2}) = - \frac{2}{3} \cdot 3$

Move the leading negative in $- \frac{3 (5 x - 3)}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 (5 x - 3)}{2} = - \frac{2}{3} \cdot 3$

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 (5 x - 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - (5 x - 3) = - \frac{2}{3} \cdot 3$

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $5 x - 3$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$5 x - 3 = - 2$

Step 6

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

Add $3$ to both sides of the equation.

$5 x = - 2 + 3$

Add $- 2$ and $3$ .

$5 x = 1$

Step 7

Divide each term in $5 x = 1$ by $5$ and simplify.

Divide each term in $5 x = 1$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.2$

Solve for x 1/2-(7x-4)=-1/2(-x-6)

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