Finite Math Examples

$4 x + 2 = (- \frac{6}{5}) (9 x - 3) + (\frac{2}{5}) (7 x - 4)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \frac{6}{5} \cdot (9 x - 3) + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2

Simplify $- \frac{6}{5} \cdot (9 x - 3) + \frac{2}{5} \cdot (7 x - 4)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- \frac{6}{5} (9 x) - \frac{6}{5} \cdot - 3 + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.2

Multiply $- \frac{6}{5} (9 x)$ .

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Step 2.1.2.1

Multiply $9$ by $- 1$ .

$- 9 (\frac{6}{5}) x - \frac{6}{5} \cdot - 3 + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.2.2

Combine $- 9$ and $\frac{6}{5}$ .

$\frac{- 9 \cdot 6}{5} x - \frac{6}{5} \cdot - 3 + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.2.3

Multiply $- 9$ by $6$ .

$\frac{- 54}{5} x - \frac{6}{5} \cdot - 3 + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.2.4

Combine $\frac{- 54}{5}$ and $x$ .

$\frac{- 54 x}{5} - \frac{6}{5} \cdot - 3 + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.3

Multiply $- \frac{6}{5} \cdot - 3$ .

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Step 2.1.3.1

Multiply $- 3$ by $- 1$ .

$\frac{- 54 x}{5} + 3 (\frac{6}{5}) + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.3.2

Combine $3$ and $\frac{6}{5}$ .

$\frac{- 54 x}{5} + \frac{3 \cdot 6}{5} + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.3.3

Multiply $3$ by $6$ .

$\frac{- 54 x}{5} + \frac{18}{5} + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.4

Move the negative in front of the fraction.

$- \frac{54 x}{5} + \frac{18}{5} + \frac{2}{5} \cdot (7 x - 4) = 4 x + 2$

Step 2.1.5

Apply the distributive property.

$- \frac{54 x}{5} + \frac{18}{5} + \frac{2}{5} (7 x) + \frac{2}{5} \cdot - 4 = 4 x + 2$

Step 2.1.6

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

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Step 2.1.6.1

Combine $7$ and $\frac{2}{5}$ .

$- \frac{54 x}{5} + \frac{18}{5} + \frac{7 \cdot 2}{5} x + \frac{2}{5} \cdot - 4 = 4 x + 2$

Step 2.1.6.2

Multiply $7$ by $2$ .

$- \frac{54 x}{5} + \frac{18}{5} + \frac{14}{5} x + \frac{2}{5} \cdot - 4 = 4 x + 2$

Step 2.1.6.3

Combine $\frac{14}{5}$ and $x$ .

$- \frac{54 x}{5} + \frac{18}{5} + \frac{14 x}{5} + \frac{2}{5} \cdot - 4 = 4 x + 2$

Step 2.1.7

Multiply $\frac{2}{5} \cdot - 4$ .

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Step 2.1.7.1

Combine $\frac{2}{5}$ and $- 4$ .

$- \frac{54 x}{5} + \frac{18}{5} + \frac{14 x}{5} + \frac{2 \cdot - 4}{5} = 4 x + 2$

Step 2.1.7.2

Multiply $2$ by $- 4$ .

$- \frac{54 x}{5} + \frac{18}{5} + \frac{14 x}{5} + \frac{- 8}{5} = 4 x + 2$

Step 2.1.8

Move the negative in front of the fraction.

$- \frac{54 x}{5} + \frac{18}{5} + \frac{14 x}{5} - \frac{8}{5} = 4 x + 2$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$\frac{- 54 x + 18 + 14 x - 8}{5} = 4 x + 2$

Step 2.2.2

Add $- 54 x$ and $14 x$ .

$\frac{- 40 x + 18 - 8}{5} = 4 x + 2$

Step 2.2.3

Subtract $8$ from $18$ .

$\frac{- 40 x + 10}{5} = 4 x + 2$

Step 2.2.4

Cancel the common factor of $- 40 x + 10$ and $5$ .

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Step 2.2.4.1

Factor $5$ out of $- 40 x$ .

$\frac{5 (- 8 x) + 10}{5} = 4 x + 2$

Step 2.2.4.2

Factor $5$ out of $10$ .

$\frac{5 (- 8 x) + 5 \cdot 2}{5} = 4 x + 2$

Step 2.2.4.3

Factor $5$ out of $5 (- 8 x) + 5 (2)$ .

$\frac{5 (- 8 x + 2)}{5} = 4 x + 2$

Step 2.2.4.4

Cancel the common factors.

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Step 2.2.4.4.1

Factor $5$ out of $5$ .

$\frac{5 (- 8 x + 2)}{5 (1)} = 4 x + 2$

Step 2.2.4.4.2

Cancel the common factor.

$\frac{5 (- 8 x + 2)}{5 \cdot 1} = 4 x + 2$

Step 2.2.4.4.3

Rewrite the expression.

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

Step 2.2.4.4.4

Divide $- 8 x + 2$ by $1$ .

$- 8 x + 2 = 4 x + 2$

Step 3

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

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Step 3.1

Subtract $4 x$ from both sides of the equation.

$- 8 x + 2 - 4 x = 2$

Step 3.2

Subtract $4 x$ from $- 8 x$ .

$- 12 x + 2 = 2$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

$- 12 x = 2 - 2$

Step 4.2

Subtract $2$ from $2$ .

$- 12 x = 0$

Step 5

Divide each term in $- 12 x = 0$ by $- 12$ and simplify.

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Step 5.1

Divide each term in $- 12 x = 0$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{0}{- 12}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 12$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{0}{- 12}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 12}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $- 12$ .

$x = 0$