Finite Math Examples

$1.9 = \frac{1}{2.6} + \frac{1}{x}$

Step 1

Rewrite the equation as $\frac{1}{2.6} + \frac{1}{x} = 1.9$ .

$\frac{1}{2.6} + \frac{1}{x} = 1.9$

Step 2

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

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Step 2.1

Subtract $\frac{1}{2.6}$ from both sides of the equation.

$\frac{1}{x} = 1.9 - \frac{1}{2.6}$

Step 2.2

Simplify each term.

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Step 2.2.1

Divide $1$ by $2.6$ .

$\frac{1}{x} = 1.9 - 1 \cdot 0.\overline{384615}$

Step 2.2.2

Multiply $- 1$ by $0.\overline{384615}$ .

$\frac{1}{x} = 1.9 - 0.\overline{384615}$

Step 2.3

Subtract $0.\overline{384615}$ from $1.9$ .

$\frac{1}{x} = 1.5\overline{153846}$

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.

$x, 1$

Step 3.2

The LCM of one and any expression is the expression.

$x$

Step 4

Multiply each term in $\frac{1}{x} = 1.5\overline{153846}$ by $x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{1}{x} = 1.5\overline{153846}$ by $x$ .

$\frac{1}{x} x = 1.5\overline{153846} x$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{1}{x} x = 1.5\overline{153846} x$

Step 4.2.1.2

Rewrite the expression.

$1 = 1.5\overline{153846} x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $1.5\overline{153846} x = 1$ .

$1.5\overline{153846} x = 1$

Step 5.2

Divide each term in $1.5\overline{153846} x = 1$ by $1.5\overline{153846}$ and simplify.

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Step 5.2.1

Divide each term in $1.5\overline{153846} x = 1$ by $1.5\overline{153846}$ .

$\frac{1.5\overline{153846} x}{1.5\overline{153846}} = \frac{1}{1.5\overline{153846}}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $1.5\overline{153846}$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{1.5\overline{153846} x}{1.5\overline{153846}} = \frac{1}{1.5\overline{153846}}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{1.5\overline{153846}}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $1$ by $1.5\overline{153846}$ .

$x = 0.65989847$