Finite Math Examples

$\frac{1}{3} \cdot (9 - 2 x) = x + 1$

Step 1

Simplify $\frac{1}{3} \cdot (9 - 2 x)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (9 - 2 x) = x + 1$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} \cdot (9 - 2 x) = x + 1$

Step 1.3

Apply the distributive property.

$\frac{1}{3} \cdot 9 + \frac{1}{3} (- 2 x) = x + 1$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $9$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

Multiply $\frac{1}{3} (- 2 x)$ .

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Step 1.5.1

Combine $- 2$ and $\frac{1}{3}$ .

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

Step 1.5.2

Combine $\frac{- 2}{3}$ and $x$ .

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

Combine $- x$ and $\frac{3}{3}$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $x$ out of $- 2 x - x \cdot 3$ .

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Step 2.5.1.1.1

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

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

Step 2.5.1.1.2

Factor $x$ out of $- x \cdot 3$ .

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

Step 2.5.1.1.3

Factor $x$ out of $x \cdot - 2 + x (- 1 \cdot 3)$ .

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

Step 2.5.1.2

Multiply $- 1$ by $3$ .

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

Step 2.5.1.3

Subtract $3$ from $- 2$ .

$3 + \frac{x \cdot - 5}{3} = 1$

Step 2.5.2

Move $- 5$ to the left of $x$ .

$3 + \frac{- 5 \cdot x}{3} = 1$

Step 2.5.3

Move the negative in front of the fraction.

$3 - \frac{5 x}{3} = 1$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$- \frac{5 x}{3} = 1 - 3$

Step 3.2

Subtract $3$ from $1$ .

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

Step 4

Multiply both sides of the equation by $- \frac{3}{5}$ .

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

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 $- \frac{3}{5} (- \frac{5 x}{3})$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

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

Step 5.1.1.1.2

Move the leading negative in $- \frac{5 x}{3}$ into the numerator.

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

Step 5.1.1.1.3

Factor $3$ out of $- 3$ .

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

Step 5.1.1.1.4

Cancel the common factor.

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

Step 5.1.1.1.5

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

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

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 5.1.1.3.2

Multiply $x$ by $1$ .

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{3}{5} \cdot - 2$ .

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Step 5.2.1.1

Multiply $- 2$ by $- 1$ .

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

Step 5.2.1.2

Combine $2$ and $\frac{3}{5}$ .

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

Step 5.2.1.3

Multiply $2$ by $3$ .

$x = \frac{6}{5}$

Step 6