Algebra Examples

$\frac{3.4}{2 x - 12} = \frac{18}{4.5}$

Step 1

Factor each term.

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Step 1.1

Factor $2$ out of $2 x - 12$ .

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Step 1.1.1

Factor $2$ out of $2 x$ .

$\frac{3.4}{2 (x) - 12} = \frac{18}{4.5}$

Step 1.1.2

Factor $2$ out of $- 12$ .

$\frac{3.4}{2 x + 2 \cdot - 6} = \frac{18}{4.5}$

Step 1.1.3

Factor $2$ out of $2 x + 2 \cdot - 6$ .

$\frac{3.4}{2 (x - 6)} = \frac{18}{4.5}$

Step 1.2

Factor $3.4$ out of $3.4$ .

$\frac{3.4 (1)}{2 (x - 6)} = \frac{18}{4.5}$

Step 1.3

Separate fractions.

$\frac{3.4}{2} \cdot \frac{1}{x - 6} = \frac{18}{4.5}$

Step 1.4

Divide $3.4$ by $2$ .

$1.7 \frac{1}{x - 6} = \frac{18}{4.5}$

Step 1.5

Combine $1.7$ and $\frac{1}{x - 6}$ .

$\frac{1.7}{x - 6} = \frac{18}{4.5}$

Step 1.6

Divide $18$ by $4.5$ .

$\frac{1.7}{x - 6} = 4$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$x - 6, 1$

Step 2.2

Remove parentheses.

$x - 6, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x - 6$

Step 3

Multiply each term in $\frac{1.7}{x - 6} = 4$ by $x - 6$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1.7}{x - 6} = 4$ by $x - 6$ .

$\frac{1.7}{x - 6} (x - 6) = 4 (x - 6)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x - 6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1.7}{x - 6} (x - 6) = 4 (x - 6)$

Step 3.2.1.2

Rewrite the expression.

$1.7 = 4 (x - 6)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$1.7 = 4 x + 4 \cdot - 6$

Step 3.3.2

Multiply $4$ by $- 6$ .

$1.7 = 4 x - 24$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $4 x - 24 = 1.7$ .

$4 x - 24 = 1.7$

Step 4.2

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

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Step 4.2.1

Add $24$ to both sides of the equation.

$4 x = 1.7 + 24$

Step 4.2.2

Add $1.7$ and $24$ .

$4 x = 25.7$

Step 4.3

Divide each term in $4 x = 25.7$ by $4$ and simplify.

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Step 4.3.1

Divide each term in $4 x = 25.7$ by $4$ .

$\frac{4 x}{4} = \frac{25.7}{4}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $4$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{25.7}{4}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{25.7}{4}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $25.7$ by $4$ .

$x = 6.425$