Finite Math Examples

$\frac{1}{8} - \frac{x + 3}{4} = \frac{3 x - 2}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{1}{8} - \frac{x + 3}{4}) \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{1}{8} - \frac{x + 3}{4}) \cdot 2$ .

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Step 2.1.1.1

To write $- \frac{x + 3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{1}{8} - \frac{x + 3}{4} \cdot \frac{2}{2}) \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.2.1

Multiply $\frac{x + 3}{4}$ by $\frac{2}{2}$ .

$(\frac{1}{8} - \frac{(x + 3) \cdot 2}{4 \cdot 2}) \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.2.2

Multiply $4$ by $2$ .

$(\frac{1}{8} - \frac{(x + 3) \cdot 2}{8}) \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.3

Combine the numerators over the common denominator.

$\frac{1 - (x + 3) \cdot 2}{8} \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.4

Simplify the numerator.

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Step 2.1.1.4.1

Apply the distributive property.

$\frac{1 + (- x - 1 \cdot 3) \cdot 2}{8} \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.4.2

Multiply $- 1$ by $3$ .

$\frac{1 + (- x - 3) \cdot 2}{8} \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.4.3

Apply the distributive property.

$\frac{1 - x \cdot 2 - 3 \cdot 2}{8} \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.4.4

Multiply $2$ by $- 1$ .

$\frac{1 - 2 x - 3 \cdot 2}{8} \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.4.5

Multiply $- 3$ by $2$ .

$\frac{1 - 2 x - 6}{8} \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.4.6

Subtract $6$ from $1$ .

$\frac{- 2 x - 5}{8} \cdot 2 = \frac{3 x - 2}{2} \cdot 2$

Step 2.1.1.5

Simplify terms.

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Step 2.1.1.5.1

Cancel the common factor of $2$ .

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Step 2.1.1.5.1.1

Factor $2$ out of $8$ .

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

Step 2.1.1.5.1.2

Cancel the common factor.

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

Step 2.1.1.5.1.3

Rewrite the expression.

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

Step 2.1.1.5.2

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

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

Step 2.1.1.5.3

Rewrite $- 5$ as $- 1 (5)$ .

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

Step 2.1.1.5.4

Factor $- 1$ out of $- (2 x) - 1 (5)$ .

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

Step 2.1.1.5.5

Simplify the expression.

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Step 2.1.1.5.5.1

Rewrite $- (2 x + 5)$ as $- 1 (2 x + 5)$ .

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

Step 2.1.1.5.5.2

Move the negative in front of the fraction.

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

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

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

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

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $4$ .

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

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 $- \frac{2 x + 5}{4} \cdot 4$ .

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Step 3.2.1.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1.1

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

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

Step 3.2.1.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.1.3

Rewrite the expression.

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

Step 3.2.1.1.2

Apply the distributive property.

$- (2 x) - 1 \cdot 5 = (3 x - 2) \cdot 4$

Step 3.2.1.1.3

Multiply.

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Step 3.2.1.1.3.1

Multiply $2$ by $- 1$ .

$- 2 x - 1 \cdot 5 = (3 x - 2) \cdot 4$

Step 3.2.1.1.3.2

Multiply $- 1$ by $5$ .

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

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(3 x - 2) \cdot 4$ .

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Step 3.2.2.1.1

Apply the distributive property.

$- 2 x - 5 = 3 x \cdot 4 - 2 \cdot 4$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $4$ by $3$ .

$- 2 x - 5 = 12 x - 2 \cdot 4$

Step 3.2.2.1.2.2

Multiply $- 2$ by $4$ .

$- 2 x - 5 = 12 x - 8$

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

Subtract $12 x$ from both sides of the equation.

$- 2 x - 5 - 12 x = - 8$

Step 3.3.1.2

Subtract $12 x$ from $- 2 x$ .

$- 14 x - 5 = - 8$

Step 3.3.2

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

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Step 3.3.2.1

Add $5$ to both sides of the equation.

$- 14 x = - 8 + 5$

Step 3.3.2.2

Add $- 8$ and $5$ .

$- 14 x = - 3$

Step 3.3.3

Divide each term in $- 14 x = - 3$ by $- 14$ and simplify.

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Step 3.3.3.1

Divide each term in $- 14 x = - 3$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{- 3}{- 14}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 14$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 3}{- 14}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{- 14}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{3}{14}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{14}$

Decimal Form:

$x = 0.2\overline{142857}$