Solve for x 14-4x=5+x/2

$14 - 4 x = 5 + \frac{x}{2}$

Step 1

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

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

$14 - 4 x - \frac{x}{2} = 5$

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

$14 - 4 x \cdot \frac{2}{2} - \frac{x}{2} = 5$

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

$14 + \frac{- 4 x \cdot 2}{2} - \frac{x}{2} = 5$

Combine the numerators over the common denominator.

$14 + \frac{- 4 x \cdot 2 - x}{2} = 5$

Simplify each term.

Simplify the numerator.

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

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

$14 + \frac{x (- 4 \cdot 2) - x}{2} = 5$

Factor $x$ out of $- x$ .

$14 + \frac{x (- 4 \cdot 2) + x \cdot - 1}{2} = 5$

Factor $x$ out of $x (- 4 \cdot 2) + x \cdot - 1$ .

$14 + \frac{x (- 4 \cdot 2 - 1)}{2} = 5$

Multiply $- 4$ by $2$ .

$14 + \frac{x (- 8 - 1)}{2} = 5$

Subtract $1$ from $- 8$ .

$14 + \frac{x \cdot - 9}{2} = 5$

Move $- 9$ to the left of $x$ .

$14 + \frac{- 9 \cdot x}{2} = 5$

Move the negative in front of the fraction.

$14 - \frac{9 x}{2} = 5$

Step 2

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

Subtract $14$ from both sides of the equation.

$- \frac{9 x}{2} = 5 - 14$

Subtract $14$ from $5$ .

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

Step 3

Multiply both sides of the equation by $- \frac{2}{9}$ .

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

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

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

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

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $9$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Simplify $- \frac{2}{9} \cdot - 9$ .

Cancel the common factor of $9$ .

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

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

Factor $9$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$x = 2$

Solve for x 14-4x=5+x/2

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