Solve for x 3.5=(4+2x)/(0.5-x)

$3.5 = \frac{4 + 2 x}{0.5 - x}$

Rewrite the equation as $\frac{4 + 2 x}{0.5 - x} = 3.5$ .

$\frac{4 + 2 x}{0.5 - x} = 3.5$

Factor each term.

Factor $2$ out of $4 + 2 x$ .

Factor $2$ out of $4$ .

$\frac{2 \cdot 2 + 2 x}{0.5 - x} = 3.5$

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

$\frac{2 \cdot (2 + x)}{0.5 - x} = 3.5$

Multiply $2$ by $2 + x$ .

$\frac{2 (2 + x)}{0.5 - x} = 3.5$

Factor $0.5$ out of $0.5 - x$ .

Factor $0.5$ out of $0.5$ .

$\frac{2 (2 + x)}{0.5 (1) - x} = 3.5$

Factor $0.5$ out of $- x$ .

$\frac{2 (2 + x)}{0.5 (1) + 0.5 (- 2 x)} = 3.5$

Factor $0.5$ out of $0.5 (1) + 0.5 (- 2 x)$ .

$\frac{2 (2 + x)}{0.5 (1 - 2 x)} = 3.5$

Separate fractions.

$\frac{2}{0.5} \cdot \frac{2 + x}{1 - 2 x} = 3.5$

Divide $2$ by $0.5$ .

$4 \frac{2 + x}{1 - 2 x} = 3.5$

Combine $4$ and $\frac{2 + x}{1 - 2 x}$ .

$\frac{4 (2 + x)}{1 - 2 x} = 3.5$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1 - 2 x, 1$

Remove parentheses.

$1 - 2 x, 1$

The LCM of one and any expression is the expression.

$1 - 2 x$

Multiply each term in $\frac{4 (2 + x)}{1 - 2 x} = 3.5$ by $1 - 2 x$ to eliminate the fractions.

Multiply each term in $\frac{4 (2 + x)}{1 - 2 x} = 3.5$ by $1 - 2 x$ .

$\frac{4 (2 + x)}{1 - 2 x} (1 - 2 x) = 3.5 (1 - 2 x)$

Simplify the left side.

Cancel the common factor of $1 - 2 x$ .

Cancel the common factor.

$\frac{4 (2 + x)}{1 - 2 x} (1 - 2 x) = 3.5 (1 - 2 x)$

Rewrite the expression.

$4 (2 + x) = 3.5 (1 - 2 x)$

Apply the distributive property.

$4 \cdot 2 + 4 x = 3.5 (1 - 2 x)$

Multiply $4$ by $2$ .

$8 + 4 x = 3.5 (1 - 2 x)$

Simplify the right side.

Apply the distributive property.

$8 + 4 x = 3.5 \cdot 1 + 3.5 (- 2 x)$

Multiply.

Multiply $3.5$ by $1$ .

$8 + 4 x = 3.5 + 3.5 (- 2 x)$

Multiply $- 2$ by $3.5$ .

$8 + 4 x = 3.5 - 7 x$

Solve the equation.

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

Add $7 x$ to both sides of the equation.

$8 + 4 x + 7 x = 3.5$

Add $4 x$ and $7 x$ .

$8 + 11 x = 3.5$

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

Subtract $8$ from both sides of the equation.

$11 x = 3.5 - 8$

Subtract $8$ from $3.5$ .

$11 x = - 4.5$

Divide each term in $11 x = - 4.5$ by $11$ and simplify.

Divide each term in $11 x = - 4.5$ by $11$ .

$\frac{11 x}{11} = \frac{- 4.5}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{- 4.5}{11}$

Divide $x$ by $1$ .

$x = \frac{- 4.5}{11}$

Simplify the right side.

Divide $- 4.5$ by $11$ .

$x = - 0.4\overline{09}$

Solve for x 3.5=(4+2x)/(0.5-x)

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