Finite Math Examples

$5 (- 3 + 1) = - 14 (x + 1)$

Step 1

Rewrite the equation as $- 14 (x + 1) = 5 (- 3 + 1)$ .

$- 14 (x + 1) = 5 (- 3 + 1)$

Step 2

Simplify.

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Step 2.1

Add $- 3$ and $1$ .

$- 14 (x + 1) = 5 \cdot - 2$

Step 2.2

Multiply $5$ by $- 2$ .

$- 14 (x + 1) = - 10$

Step 3

Divide each term in $- 14 (x + 1) = - 10$ by $- 14$ and simplify.

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Step 3.1

Divide each term in $- 14 (x + 1) = - 10$ by $- 14$ .

$\frac{- 14 (x + 1)}{- 14} = \frac{- 10}{- 14}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 14$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 14 (x + 1)}{- 14} = \frac{- 10}{- 14}$

Step 3.2.1.2

Divide $x + 1$ by $1$ .

$x + 1 = \frac{- 10}{- 14}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $- 10$ and $- 14$ .

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Step 3.3.1.1

Factor $- 2$ out of $- 10$ .

$x + 1 = \frac{- 2 (5)}{- 14}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $- 2$ out of $- 14$ .

$x + 1 = \frac{- 2 \cdot 5}{- 2 \cdot 7}$

Step 3.3.1.2.2

Cancel the common factor.

$x + 1 = \frac{- 2 \cdot 5}{- 2 \cdot 7}$

Step 3.3.1.2.3

Rewrite the expression.

$x + 1 = \frac{5}{7}$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$x = \frac{5}{7} - 1$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = \frac{5}{7} - 1 \cdot \frac{7}{7}$

Step 4.3

Combine $- 1$ and $\frac{7}{7}$ .

$x = \frac{5}{7} + \frac{- 1 \cdot 7}{7}$

Step 4.4

Combine the numerators over the common denominator.

$x = \frac{5 - 1 \cdot 7}{7}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $7$ .

$x = \frac{5 - 7}{7}$

Step 4.5.2

Subtract $7$ from $5$ .

$x = \frac{- 2}{7}$

Step 4.6

Move the negative in front of the fraction.

$x = - \frac{2}{7}$

Step 5