Algebra Examples

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

Step 1

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

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

Step 2

Factor each term.

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Step 2.1

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

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Step 2.1.1

Factor $2$ out of $4$ .

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

Step 2.1.2

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

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

Step 2.1.3

Multiply $2$ by $2 + x$ .

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

Step 2.2

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

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Step 2.2.1

Factor $0.5$ out of $0.5$ .

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

Step 2.2.2

Factor $0.5$ out of $- x$ .

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

Step 2.2.3

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

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

Step 2.3

Separate fractions.

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

Step 2.4

Divide $2$ by $0.5$ .

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

Step 2.5

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

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

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$1 - 2 x, 1$

Step 3.2

Remove parentheses.

$1 - 2 x, 1$

Step 3.3

The LCM of one and any expression is the expression.

$1 - 2 x$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Rewrite the expression.

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

Step 4.2.2

Apply the distributive property.

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

Step 4.2.3

Multiply $4$ by $2$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

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

Step 4.3.2

Multiply.

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Step 4.3.2.1

Multiply $3.5$ by $1$ .

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

Step 4.3.2.2

Multiply $- 2$ by $3.5$ .

$8 + 4 x = 3.5 - 7 x$

Step 5

Solve the equation.

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Step 5.1

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

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Step 5.1.1

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

$8 + 4 x + 7 x = 3.5$

Step 5.1.2

Add $4 x$ and $7 x$ .

$8 + 11 x = 3.5$

Step 5.2

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

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Step 5.2.1

Subtract $8$ from both sides of the equation.

$11 x = 3.5 - 8$

Step 5.2.2

Subtract $8$ from $3.5$ .

$11 x = - 4.5$

Step 5.3

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

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Step 5.3.1

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

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

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $11$ .

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Step 5.3.2.1.1

Cancel the common factor.

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

Step 5.3.2.1.2

Divide $x$ by $1$ .

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

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $- 4.5$ by $11$ .

$x = - 0.4\overline{09}$