Finite Math Examples

$- \frac{23}{5} (x + 8) = \frac{1}{5} x - 15$

Step 1

Simplify $- \frac{23}{5} \cdot (x + 8)$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{23}{5} \cdot (x + 8) = \frac{1}{5} x - 15$

Step 1.2

Simplify by adding zeros.

$- \frac{23}{5} \cdot (x + 8) = \frac{1}{5} x - 15$

Step 1.3

Apply the distributive property.

$- \frac{23}{5} x - \frac{23}{5} \cdot 8 = \frac{1}{5} x - 15$

Step 1.4

Combine $x$ and $\frac{23}{5}$ .

$- \frac{x \cdot 23}{5} - \frac{23}{5} \cdot 8 = \frac{1}{5} x - 15$

Step 1.5

Multiply $- \frac{23}{5} \cdot 8$ .

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Step 1.5.1

Multiply $8$ by $- 1$ .

$- \frac{x \cdot 23}{5} - 8 (\frac{23}{5}) = \frac{1}{5} x - 15$

Step 1.5.2

Combine $- 8$ and $\frac{23}{5}$ .

$- \frac{x \cdot 23}{5} + \frac{- 8 \cdot 23}{5} = \frac{1}{5} x - 15$

Step 1.5.3

Multiply $- 8$ by $23$ .

$- \frac{x \cdot 23}{5} + \frac{- 184}{5} = \frac{1}{5} x - 15$

Step 1.6

Simplify each term.

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Step 1.6.1

Move $23$ to the left of $x$ .

$- \frac{23 \cdot x}{5} + \frac{- 184}{5} = \frac{1}{5} x - 15$

Step 1.6.2

Move the negative in front of the fraction.

$- \frac{23 x}{5} - \frac{184}{5} = \frac{1}{5} x - 15$

Step 2

Combine $\frac{1}{5}$ and $x$ .

$- \frac{23 x}{5} - \frac{184}{5} = \frac{x}{5} - 15$

Step 3

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

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Step 3.1

Subtract $\frac{x}{5}$ from both sides of the equation.

$- \frac{23 x}{5} - \frac{184}{5} - \frac{x}{5} = - 15$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 23 x - 184 - x}{5} = - 15$

Step 3.3

Subtract $x$ from $- 23 x$ .

$\frac{- 24 x - 184}{5} = - 15$

Step 3.4

Factor $8$ out of $- 24 x - 184$ .

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Step 3.4.1

Factor $8$ out of $- 24 x$ .

$\frac{8 (- 3 x) - 184}{5} = - 15$

Step 3.4.2

Factor $8$ out of $- 184$ .

$\frac{8 (- 3 x) + 8 (- 23)}{5} = - 15$

Step 3.4.3

Factor $8$ out of $8 (- 3 x) + 8 (- 23)$ .

$\frac{8 (- 3 x - 23)}{5} = - 15$

Step 3.5

Factor $- 1$ out of $- 3 x$ .

$\frac{8 (- (3 x) - 23)}{5} = - 15$

Step 3.6

Rewrite $- 23$ as $- 1 (23)$ .

$\frac{8 (- (3 x) - 1 (23))}{5} = - 15$

Step 3.7

Factor $- 1$ out of $- (3 x) - 1 (23)$ .

$\frac{8 (- (3 x + 23))}{5} = - 15$

Step 3.8

Rewrite $- (3 x + 23)$ as $- 1 (3 x + 23)$ .

$\frac{8 (- 1 (3 x + 23))}{5} = - 15$

Step 3.9

Move the negative in front of the fraction.

$- \frac{8 (3 x + 23)}{5} = - 15$

Step 4

Multiply both sides of the equation by $- \frac{5}{8}$ .

$- \frac{5}{8} (- \frac{8 (3 x + 23)}{5}) = - \frac{5}{8} \cdot - 15$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{5}{8} (- \frac{8 (3 x + 23)}{5})$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$\frac{- 5}{8} (- \frac{8 (3 x + 23)}{5}) = - \frac{5}{8} \cdot - 15$

Step 5.1.1.1.2

Move the leading negative in $- \frac{8 (3 x + 23)}{5}$ into the numerator.

$\frac{- 5}{8} \cdot \frac{- 8 (3 x + 23)}{5} = - \frac{5}{8} \cdot - 15$

Step 5.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{8} \cdot \frac{- 8 (3 x + 23)}{5} = - \frac{5}{8} \cdot - 15$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{8} \cdot \frac{- 8 (3 x + 23)}{5} = - \frac{5}{8} \cdot - 15$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{8} (- 8 (3 x + 23)) = - \frac{5}{8} \cdot - 15$

Step 5.1.1.2

Cancel the common factor of $8$ .

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Step 5.1.1.2.1

Factor $8$ out of $- 8 (3 x + 23)$ .

$\frac{- 1}{8} (8 (- (3 x + 23))) = - \frac{5}{8} \cdot - 15$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{8} (8 (- (3 x + 23))) = - \frac{5}{8} \cdot - 15$

Step 5.1.1.2.3

Rewrite the expression.

$- - (3 x + 23) = - \frac{5}{8} \cdot - 15$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (3 x + 23) = - \frac{5}{8} \cdot - 15$

Step 5.1.1.3.2

Multiply $3 x + 23$ by $1$ .

$3 x + 23 = - \frac{5}{8} \cdot - 15$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{5}{8} \cdot - 15$ .

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Step 5.2.1.1

Multiply $- 15$ by $- 1$ .

$3 x + 23 = 15 (\frac{5}{8})$

Step 5.2.1.2

Combine $15$ and $\frac{5}{8}$ .

$3 x + 23 = \frac{15 \cdot 5}{8}$

Step 5.2.1.3

Multiply $15$ by $5$ .

$3 x + 23 = \frac{75}{8}$

Step 6

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

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Step 6.1

Subtract $23$ from both sides of the equation.

$3 x = \frac{75}{8} - 23$

Step 6.2

To write $- 23$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$3 x = \frac{75}{8} - 23 \cdot \frac{8}{8}$

Step 6.3

Combine $- 23$ and $\frac{8}{8}$ .

$3 x = \frac{75}{8} + \frac{- 23 \cdot 8}{8}$

Step 6.4

Combine the numerators over the common denominator.

$3 x = \frac{75 - 23 \cdot 8}{8}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 23$ by $8$ .

$3 x = \frac{75 - 184}{8}$

Step 6.5.2

Subtract $184$ from $75$ .

$3 x = \frac{- 109}{8}$

Step 6.6

Move the negative in front of the fraction.

$3 x = - \frac{109}{8}$

Step 7

Divide each term in $3 x = - \frac{109}{8}$ by $3$ and simplify.

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Step 7.1

Divide each term in $3 x = - \frac{109}{8}$ by $3$ .

$\frac{3 x}{3} = \frac{- \frac{109}{8}}{3}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $3$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \frac{109}{8}}{3}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{109}{8}}{3}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{109}{8} \cdot \frac{1}{3}$

Step 7.3.2

Multiply $- \frac{109}{8} \cdot \frac{1}{3}$ .

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Step 7.3.2.1

Multiply $\frac{1}{3}$ by $\frac{109}{8}$ .

$x = - \frac{109}{3 \cdot 8}$

Step 7.3.2.2

Multiply $3$ by $8$ .

$x = - \frac{109}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{109}{24}$

Decimal Form:

$x = - 4.541\overline{6}$

Mixed Number Form:

$x = - 4 \frac{13}{24}$