Pre-Algebra Examples

- \frac{14}{17} x + \frac{13}{17} = \frac{12}{17}

$- \frac{14}{17} x + \frac{13}{17} = \frac{12}{17}$

Step 1

Simplify each term.

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Step 1.1

Combine

x

$x$ and

\frac{14}{17}

$\frac{14}{17}$ .

- \frac{x \cdot 14}{17} + \frac{13}{17} = \frac{12}{17}

$- \frac{x \cdot 14}{17} + \frac{13}{17} = \frac{12}{17}$

Step 1.2

Move

14

$14$ to the left of

x

$x$ .

- \frac{14 x}{17} + \frac{13}{17} = \frac{12}{17}

$- \frac{14 x}{17} + \frac{13}{17} = \frac{12}{17}$

- \frac{14 x}{17} + \frac{13}{17} = \frac{12}{17}

$- \frac{14 x}{17} + \frac{13}{17} = \frac{12}{17}$

Step 2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.1

Subtract

\frac{13}{17}

$\frac{13}{17}$ from both sides of the equation.

- \frac{14 x}{17} = \frac{12}{17} - \frac{13}{17}

$- \frac{14 x}{17} = \frac{12}{17} - \frac{13}{17}$

Step 2.2

Combine the numerators over the common denominator.

- \frac{14 x}{17} = \frac{12 - 13}{17}

$- \frac{14 x}{17} = \frac{12 - 13}{17}$

Step 2.3

Subtract

13

$13$ from

12

$12$ .

- \frac{14 x}{17} = \frac{- 1}{17}

$- \frac{14 x}{17} = \frac{- 1}{17}$

Step 2.4

Move the negative in front of the fraction.

- \frac{14 x}{17} = - \frac{1}{17}

$- \frac{14 x}{17} = - \frac{1}{17}$

- \frac{14 x}{17} = - \frac{1}{17}

$- \frac{14 x}{17} = - \frac{1}{17}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

- 14 x = - 1

$- 14 x = - 1$

Step 4

Divide each term in

- 14 x = - 1

$- 14 x = - 1$ by

- 14

$- 14$ and simplify.

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Step 4.1

Divide each term in

- 14 x = - 1

$- 14 x = - 1$ by

- 14

$- 14$ .

\frac{- 14 x}{- 14} = \frac{- 1}{- 14}

$\frac{- 14 x}{- 14} = \frac{- 1}{- 14}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

- 14

$- 14$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 1}{- 14}$

Step 4.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{- 1}{- 14}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{14}$

Decimal Form:

$x = 0.0\overline{714285}$