Finite Math Examples

$- 5 x + 10 y = - \frac{x}{3} + 2$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$- 5 x + 10 (0) = - \frac{x}{3} + 2$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $- 5 x + 10 (0)$ .

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Step 1.2.1.1

Multiply $10$ by $0$ .

$- 5 x + 0 = - \frac{x}{3} + 2$

Step 1.2.1.2

Add $- 5 x$ and $0$ .

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

Step 1.2.2

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

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Step 1.2.2.1

Add $\frac{x}{3}$ to both sides of the equation.

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

Step 1.2.2.2

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.2.2.3

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

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

Step 1.2.2.4

Combine the numerators over the common denominator.

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

Step 1.2.2.5

Simplify the numerator.

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Step 1.2.2.5.1

Factor $x$ out of $- 5 x \cdot 3 + x$ .

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Step 1.2.2.5.1.1

Factor $x$ out of $- 5 x \cdot 3$ .

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

Step 1.2.2.5.1.2

Raise $x$ to the power of $1$ .

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

Step 1.2.2.5.1.3

Factor $x$ out of $x^{1}$ .

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

Step 1.2.2.5.1.4

Factor $x$ out of $x (- 5 \cdot 3) + x \cdot 1$ .

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

Step 1.2.2.5.2

Multiply $- 5$ by $3$ .

$\frac{x (- 15 + 1)}{3} = 2$

Step 1.2.2.5.3

Add $- 15$ and $1$ .

$\frac{x \cdot - 14}{3} = 2$

Step 1.2.2.6

Move $- 14$ to the left of $x$ .

$\frac{- 14 \cdot x}{3} = 2$

Step 1.2.2.7

Move the negative in front of the fraction.

$- \frac{14 x}{3} = 2$

Step 1.2.3

Multiply both sides of the equation by $- \frac{3}{14}$ .

$- \frac{3}{14} (- \frac{14 x}{3}) = - \frac{3}{14} \cdot 2$

Step 1.2.4

Simplify both sides of the equation.

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Step 1.2.4.1

Simplify the left side.

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Step 1.2.4.1.1

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

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Step 1.2.4.1.1.1

Cancel the common factor of $3$ .

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Step 1.2.4.1.1.1.1

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

$\frac{- 3}{14} (- \frac{14 x}{3}) = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.1.2

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

$\frac{- 3}{14} \cdot \frac{- 14 x}{3} = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{14} \cdot \frac{- 14 x}{3} = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{14} \cdot \frac{- 14 x}{3} = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{14} (- 14 x) = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.2

Cancel the common factor of $14$ .

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Step 1.2.4.1.1.2.1

Factor $14$ out of $- 14 x$ .

$\frac{- 1}{14} (14 (- x)) = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{14} (14 (- x)) = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.3

Multiply.

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Step 1.2.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{14} \cdot 2$

Step 1.2.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{14} \cdot 2$

Step 1.2.4.2

Simplify the right side.

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Step 1.2.4.2.1

Simplify $- \frac{3}{14} \cdot 2$ .

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Step 1.2.4.2.1.1

Cancel the common factor of $2$ .

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Step 1.2.4.2.1.1.1

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

$x = \frac{- 3}{14} \cdot 2$

Step 1.2.4.2.1.1.2

Factor $2$ out of $14$ .

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

Step 1.2.4.2.1.1.3

Cancel the common factor.

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

Step 1.2.4.2.1.1.4

Rewrite the expression.

$x = \frac{- 3}{7}$

Step 1.2.4.2.1.2

Move the negative in front of the fraction.

$x = - \frac{3}{7}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{3}{7}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$- 5 \cdot 0 + 10 y = - \frac{0}{3} + 2$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $- 5 \cdot 0 + 10 y$ .

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Step 2.2.1.1

Multiply $- 5$ by $0$ .

$0 + 10 y = - \frac{0}{3} + 2$

Step 2.2.1.2

Add $0$ and $10 y$ .

$10 y = - \frac{0}{3} + 2$

Step 2.2.2

Simplify $- \frac{0}{3} + 2$ .

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Step 2.2.2.1

Simplify each term.

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Step 2.2.2.1.1

Divide $0$ by $3$ .

$10 y = - 0 + 2$

Step 2.2.2.1.2

Multiply $- 1$ by $0$ .

$10 y = 0 + 2$

Step 2.2.2.2

Add $0$ and $2$ .

$10 y = 2$

Step 2.2.3

Divide each term in $10 y = 2$ by $10$ and simplify.

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Step 2.2.3.1

Divide each term in $10 y = 2$ by $10$ .

$\frac{10 y}{10} = \frac{2}{10}$

Step 2.2.3.2

Simplify the left side.

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Step 2.2.3.2.1

Cancel the common factor of $10$ .

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Step 2.2.3.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{2}{10}$

Step 2.2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{10}$

Step 2.2.3.3

Simplify the right side.

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Step 2.2.3.3.1

Cancel the common factor of $2$ and $10$ .

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Step 2.2.3.3.1.1

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{10}$

Step 2.2.3.3.1.2

Cancel the common factors.

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Step 2.2.3.3.1.2.1

Factor $2$ out of $10$ .

$y = \frac{2 \cdot 1}{2 \cdot 5}$

Step 2.2.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot 5}$

Step 2.2.3.3.1.2.3

Rewrite the expression.

$y = \frac{1}{5}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{5})$

Step 3

List the intersections.

x-intercept(s): $(- \frac{3}{7}, 0)$

y-intercept(s): $(0, \frac{1}{5})$

Step 4