Solve for x 3-(4x+1/2)=1/2(x-10)

$3 - (4 x + \frac{1}{2}) = \frac{1}{2} (x - 10)$

Simplify $3 - (4 x + \frac{1}{2})$ .

Simplify each term.

Apply the distributive property.

$3 - (4 x) - \frac{1}{2} = \frac{1}{2} \cdot (x - 10)$

Multiply $4$ by $- 1$ .

$3 - 4 x - \frac{1}{2} = \frac{1}{2} \cdot (x - 10)$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 4 x + 3 \cdot \frac{2}{2} - \frac{1}{2} = \frac{1}{2} \cdot (x - 10)$

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

$- 4 x + \frac{3 \cdot 2}{2} - \frac{1}{2} = \frac{1}{2} \cdot (x - 10)$

Combine the numerators over the common denominator.

$- 4 x + \frac{3 \cdot 2 - 1}{2} = \frac{1}{2} \cdot (x - 10)$

Simplify the numerator.

Multiply $3$ by $2$ .

$- 4 x + \frac{6 - 1}{2} = \frac{1}{2} \cdot (x - 10)$

Subtract $1$ from $6$ .

$- 4 x + \frac{5}{2} = \frac{1}{2} \cdot (x - 10)$

Simplify $\frac{1}{2} \cdot (x - 10)$ .

Apply the distributive property.

$- 4 x + \frac{5}{2} = \frac{1}{2} x + \frac{1}{2} \cdot - 10$

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

$- 4 x + \frac{5}{2} = \frac{x}{2} + \frac{1}{2} \cdot - 10$

Cancel the common factor of $2$ .

Factor $2$ out of $- 10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

Multiply $2$ by $- 4$ .

$\frac{- 8 x - x + 5}{2} = - 5$

Subtract $x$ from $- 8 x$ .

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

Factor $- 1$ out of $- 9 x$ .

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

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

$\frac{- (9 x) - 1 (- 5)}{2} = - 5$

Factor $- 1$ out of $- (9 x) - 1 (- 5)$ .

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

Rewrite $- (9 x - 5)$ as $- 1 (9 x - 5)$ .

$\frac{- 1 (9 x - 5)}{2} = - 5$

Move the negative in front of the fraction.

$- \frac{9 x - 5}{2} = - 5$

Multiply both sides of the equation by $- 2$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{9 x - 5}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{9 x - 5}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- (9 x - 5)}{2} = - 2 \cdot - 5$

Cancel the common factor.

$2 \cdot - 1 \frac{- (9 x - 5)}{2} = - 2 \cdot - 5$

Rewrite the expression.

$- - (9 x - 5) = - 2 \cdot - 5$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (9 x - 5) = - 2 \cdot - 5$

Multiply $9 x - 5$ by $1$ .

$9 x - 5 = - 2 \cdot - 5$

Simplify the right side.

Multiply $- 2$ by $- 5$ .

$9 x - 5 = 10$

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

Add $5$ to both sides of the equation.

$9 x = 10 + 5$

Add $10$ and $5$ .

$9 x = 15$

Divide each term in $9 x = 15$ by $9$ and simplify.

Divide each term in $9 x = 15$ by $9$ .

$\frac{9 x}{9} = \frac{15}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{15}{9}$

Divide $x$ by $1$ .

$x = \frac{15}{9}$

Simplify the right side.

Cancel the common factor of $15$ and $9$ .

Factor $3$ out of $15$ .

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

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.\overline{6}$

Mixed Number Form:

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

Solve for x 3-(4x+1/2)=1/2(x-10)

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