Finite Math Examples

$\frac{- 4 x + 5}{5} + \frac{9}{5} = - \frac{3 x}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{- 4 x + 5}{5} + \frac{9}{5}) \cdot 2 = - \frac{3 x}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{- 4 x + 5}{5} + \frac{9}{5}) \cdot 2$ .

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Step 2.1.1.1

Combine the numerators over the common denominator.

$\frac{- 4 x + 5 + 9}{5} \cdot 2 = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.2

Add $5$ and $9$ .

$\frac{- 4 x + 14}{5} \cdot 2 = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.3

Factor $2$ out of $- 4 x + 14$ .

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Step 2.1.1.3.1

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

$\frac{2 (- 2 x) + 14}{5} \cdot 2 = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.3.2

Factor $2$ out of $14$ .

$\frac{2 (- 2 x) + 2 (7)}{5} \cdot 2 = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.3.3

Factor $2$ out of $2 (- 2 x) + 2 (7)$ .

$\frac{2 (- 2 x + 7)}{5} \cdot 2 = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.4

Multiply $\frac{2 (- 2 x + 7)}{5} \cdot 2$ .

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Step 2.1.1.4.1

Combine $\frac{2 (- 2 x + 7)}{5}$ and $2$ .

$\frac{2 (- 2 x + 7) \cdot 2}{5} = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.4.2

Multiply $2$ by $2$ .

$\frac{4 (- 2 x + 7)}{5} = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.5

Factor $- 1$ out of $- 2 x$ .

$\frac{4 (- (2 x) + 7)}{5} = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.6

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{4 (- (2 x) - 1 (- 7))}{5} = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.7

Factor $- 1$ out of $- (2 x) - 1 (- 7)$ .

$\frac{4 (- (2 x - 7))}{5} = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.8

Simplify the expression.

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Step 2.1.1.8.1

Rewrite $- (2 x - 7)$ as $- 1 (2 x - 7)$ .

$\frac{4 (- 1 (2 x - 7))}{5} = - \frac{3 x}{2} \cdot 2$

Step 2.1.1.8.2

Move the negative in front of the fraction.

$- \frac{4 (2 x - 7)}{5} = - \frac{3 x}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$- \frac{4 (2 x - 7)}{5} = \frac{- 3 x}{2} \cdot 2$

Step 2.2.1.2

Cancel the common factor.

$- \frac{4 (2 x - 7)}{5} = \frac{- 3 x}{2} \cdot 2$

Step 2.2.1.3

Rewrite the expression.

$- \frac{4 (2 x - 7)}{5} = - 3 x$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $5$ .

$- \frac{4 (2 x - 7)}{5} \cdot 5 = - 3 x \cdot 5$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $- \frac{4 (2 x - 7)}{5} \cdot 5$ .

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Step 3.2.1.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1.1

Move the leading negative in $- \frac{4 (2 x - 7)}{5}$ into the numerator.

$\frac{- 4 (2 x - 7)}{5} \cdot 5 = - 3 x \cdot 5$

Step 3.2.1.1.1.2

Cancel the common factor.

$\frac{- 4 (2 x - 7)}{5} \cdot 5 = - 3 x \cdot 5$

Step 3.2.1.1.1.3

Rewrite the expression.

$- 4 (2 x - 7) = - 3 x \cdot 5$

Step 3.2.1.1.2

Apply the distributive property.

$- 4 (2 x) - 4 \cdot - 7 = - 3 x \cdot 5$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $2$ by $- 4$ .

$- 8 x - 4 \cdot - 7 = - 3 x \cdot 5$

Step 3.2.1.1.3.2

Multiply $- 4$ by $- 7$ .

$- 8 x + 28 = - 3 x \cdot 5$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $5$ by $- 3$ .

$- 8 x + 28 = - 15 x$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $15 x$ to both sides of the equation.

$- 8 x + 28 + 15 x = 0$

Step 3.3.1.2

Add $- 8 x$ and $15 x$ .

$7 x + 28 = 0$

Step 3.3.2

Subtract $28$ from both sides of the equation.

$7 x = - 28$

Step 3.3.3

Divide each term in $7 x = - 28$ by $7$ and simplify.

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Step 3.3.3.1

Divide each term in $7 x = - 28$ by $7$ .

$\frac{7 x}{7} = \frac{- 28}{7}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 28}{7}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 28}{7}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $- 28$ by $7$ .

$x = - 4$