Finite Math Examples

$\frac{- 2 x + 3}{3} + \frac{5}{3} = - \frac{6 x}{7}$

Step 1

Multiply both sides by $7$ .

$(\frac{- 2 x + 3}{3} + \frac{5}{3}) \cdot 7 = - \frac{6 x}{7} \cdot 7$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Combine the numerators over the common denominator.

$\frac{- 2 x + 3 + 5}{3} \cdot 7 = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.2

Add $3$ and $5$ .

$\frac{- 2 x + 8}{3} \cdot 7 = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.3

Factor $2$ out of $- 2 x + 8$ .

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Step 2.1.1.3.1

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

$\frac{2 (- x) + 8}{3} \cdot 7 = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.3.2

Factor $2$ out of $8$ .

$\frac{2 (- x) + 2 (4)}{3} \cdot 7 = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.3.3

Factor $2$ out of $2 (- x) + 2 (4)$ .

$\frac{2 (- x + 4)}{3} \cdot 7 = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.4

Multiply $\frac{2 (- x + 4)}{3} \cdot 7$ .

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Step 2.1.1.4.1

Combine $\frac{2 (- x + 4)}{3}$ and $7$ .

$\frac{2 (- x + 4) \cdot 7}{3} = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.4.2

Multiply $7$ by $2$ .

$\frac{14 (- x + 4)}{3} = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.5

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

$\frac{14 (- (x) + 4)}{3} = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.6

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{14 (- (x) - 1 (- 4))}{3} = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.7

Factor $- 1$ out of $- (x) - 1 (- 4)$ .

$\frac{14 (- (x - 4))}{3} = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.8

Simplify the expression.

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Step 2.1.1.8.1

Rewrite $- (x - 4)$ as $- 1 (x - 4)$ .

$\frac{14 (- 1 (x - 4))}{3} = - \frac{6 x}{7} \cdot 7$

Step 2.1.1.8.2

Move the negative in front of the fraction.

$- \frac{14 (x - 4)}{3} = - \frac{6 x}{7} \cdot 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Move the leading negative in $- \frac{6 x}{7}$ into the numerator.

$- \frac{14 (x - 4)}{3} = \frac{- 6 x}{7} \cdot 7$

Step 2.2.1.2

Cancel the common factor.

$- \frac{14 (x - 4)}{3} = \frac{- 6 x}{7} \cdot 7$

Step 2.2.1.3

Rewrite the expression.

$- \frac{14 (x - 4)}{3} = - 6 x$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $3$ .

$- \frac{14 (x - 4)}{3} \cdot 3 = - 6 x \cdot 3$

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

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Step 3.2.1.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1.1

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

$\frac{- 14 (x - 4)}{3} \cdot 3 = - 6 x \cdot 3$

Step 3.2.1.1.1.2

Cancel the common factor.

$\frac{- 14 (x - 4)}{3} \cdot 3 = - 6 x \cdot 3$

Step 3.2.1.1.1.3

Rewrite the expression.

$- 14 (x - 4) = - 6 x \cdot 3$

Step 3.2.1.1.2

Apply the distributive property.

$- 14 x - 14 \cdot - 4 = - 6 x \cdot 3$

Step 3.2.1.1.3

Multiply $- 14$ by $- 4$ .

$- 14 x + 56 = - 6 x \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $3$ by $- 6$ .

$- 14 x + 56 = - 18 x$

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 $18 x$ to both sides of the equation.

$- 14 x + 56 + 18 x = 0$

Step 3.3.1.2

Add $- 14 x$ and $18 x$ .

$4 x + 56 = 0$

Step 3.3.2

Subtract $56$ from both sides of the equation.

$4 x = - 56$

Step 3.3.3

Divide each term in $4 x = - 56$ by $4$ and simplify.

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Step 3.3.3.1

Divide each term in $4 x = - 56$ by $4$ .

$\frac{4 x}{4} = \frac{- 56}{4}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $4$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 56}{4}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 56}{4}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Divide $- 56$ by $4$ .

$x = - 14$