Finite Math Examples

$\frac{12 + x}{- 4} = \frac{5 x - 7}{3} + 7$

Step 1

Multiply both sides by $- 4$ .

$\frac{12 + x}{- 4} \cdot - 4 = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{12 + x}{- 4} \cdot - 4$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1.1.1

Factor $4$ out of $- 4$ .

$\frac{12 + x}{4 (- 1)} \cdot - 4 = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.1.2

Factor $4$ out of $- 4$ .

$\frac{12 + x}{4 \cdot - 1} \cdot (4 \cdot - 1) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.1.3

Cancel the common factor.

$\frac{12 + x}{4 \cdot - 1} \cdot (4 \cdot - 1) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.1.4

Rewrite the expression.

$\frac{12 + x}{- 1} \cdot - 1 = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.2

Combine $\frac{12 + x}{- 1}$ and $- 1$ .

$\frac{(12 + x) \cdot - 1}{- 1} = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.3

Simplify the expression.

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Step 2.1.1.1.3.1

Move the negative one from the denominator of $\frac{(12 + x) \cdot - 1}{- 1}$ .

$- 1 \cdot ((12 + x) \cdot - 1) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.3.2

Rewrite $- 1 \cdot ((12 + x) \cdot - 1)$ as $- ((12 + x) \cdot - 1)$ .

$- ((12 + x) \cdot - 1) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.4

Apply the distributive property.

$- (12 \cdot - 1 + x \cdot - 1) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.5

Simplify the expression.

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Step 2.1.1.1.5.1

Multiply $12$ by $- 1$ .

$- (- 12 + x \cdot - 1) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.1.5.2

Move $- 1$ to the left of $x$ .

$- (- 12 - 1 \cdot x) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.2

Rewrite $- 1 x$ as $- x$ .

$- (- 12 - x) = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.3

Simplify by multiplying through.

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Step 2.1.1.3.1

Apply the distributive property.

$- - 12 - - x = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.3.2

Multiply $- 1$ by $- 12$ .

$12 - - x = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.4

Multiply $- - x$ .

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$12 + 1 x = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.4.2

Multiply $x$ by $1$ .

$12 + x = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.1.1.5

Reorder $12$ and $x$ .

$x + 12 = (\frac{5 x - 7}{3} + 7) \cdot - 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{5 x - 7}{3} + 7) \cdot - 4$ .

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Step 2.2.1.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x + 12 = (\frac{5 x - 7}{3} + 7 \cdot \frac{3}{3}) \cdot - 4$

Step 2.2.1.2

Simplify terms.

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Step 2.2.1.2.1

Combine $7$ and $\frac{3}{3}$ .

$x + 12 = (\frac{5 x - 7}{3} + \frac{7 \cdot 3}{3}) \cdot - 4$

Step 2.2.1.2.2

Combine the numerators over the common denominator.

$x + 12 = \frac{5 x - 7 + 7 \cdot 3}{3} \cdot - 4$

Step 2.2.1.3

Simplify the numerator.

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Step 2.2.1.3.1

Multiply $7$ by $3$ .

$x + 12 = \frac{5 x - 7 + 21}{3} \cdot - 4$

Step 2.2.1.3.2

Add $- 7$ and $21$ .

$x + 12 = \frac{5 x + 14}{3} \cdot - 4$

Step 2.2.1.4

Combine fractions.

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Step 2.2.1.4.1

Combine $\frac{5 x + 14}{3}$ and $- 4$ .

$x + 12 = \frac{(5 x + 14) \cdot - 4}{3}$

Step 2.2.1.4.2

Simplify the expression.

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Step 2.2.1.4.2.1

Move $- 4$ to the left of $5 x + 14$ .

$x + 12 = \frac{- 4 \cdot (5 x + 14)}{3}$

Step 2.2.1.4.2.2

Move the negative in front of the fraction.

$x + 12 = - \frac{4 (5 x + 14)}{3}$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $3$ .

$(x + 12) \cdot 3 = - \frac{4 (5 x + 14)}{3} \cdot 3$

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 $(x + 12) \cdot 3$ .

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Step 3.2.1.1.1

Apply the distributive property.

$x \cdot 3 + 12 \cdot 3 = - \frac{4 (5 x + 14)}{3} \cdot 3$

Step 3.2.1.1.2

Simplify the expression.

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Step 3.2.1.1.2.1

Move $3$ to the left of $x$ .

$3 \cdot x + 12 \cdot 3 = - \frac{4 (5 x + 14)}{3} \cdot 3$

Step 3.2.1.1.2.2

Multiply $12$ by $3$ .

$3 x + 36 = - \frac{4 (5 x + 14)}{3} \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $- \frac{4 (5 x + 14)}{3} \cdot 3$ .

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Step 3.2.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1.1

Move the leading negative in $- \frac{4 (5 x + 14)}{3}$ into the numerator.

$3 x + 36 = \frac{- 4 (5 x + 14)}{3} \cdot 3$

Step 3.2.2.1.1.2

Cancel the common factor.

$3 x + 36 = \frac{- 4 (5 x + 14)}{3} \cdot 3$

Step 3.2.2.1.1.3

Rewrite the expression.

$3 x + 36 = - 4 (5 x + 14)$

Step 3.2.2.1.2

Apply the distributive property.

$3 x + 36 = - 4 (5 x) - 4 \cdot 14$

Step 3.2.2.1.3

Multiply.

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Step 3.2.2.1.3.1

Multiply $5$ by $- 4$ .

$3 x + 36 = - 20 x - 4 \cdot 14$

Step 3.2.2.1.3.2

Multiply $- 4$ by $14$ .

$3 x + 36 = - 20 x - 56$

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 $20 x$ to both sides of the equation.

$3 x + 36 + 20 x = - 56$

Step 3.3.1.2

Add $3 x$ and $20 x$ .

$23 x + 36 = - 56$

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

Subtract $36$ from both sides of the equation.

$23 x = - 56 - 36$

Step 3.3.2.2

Subtract $36$ from $- 56$ .

$23 x = - 92$

Step 3.3.3

Divide each term in $23 x = - 92$ by $23$ and simplify.

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Step 3.3.3.1

Divide each term in $23 x = - 92$ by $23$ .

$\frac{23 x}{23} = \frac{- 92}{23}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $23$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{23 x}{23} = \frac{- 92}{23}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 92}{23}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $- 92$ by $23$ .

$x = - 4$