Finite Math Examples

$\frac{(3 x + 4) \cdot (3 x + 11)}{(7 x + 2) \cdot (x + 5)} = y$

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 $x$ .

$\frac{(3 x + 4) \cdot (3 x + 11)}{(7 x + 2) \cdot (x + 5)} = 0$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$(3 x + 4) \cdot (3 x + 11) = 0$

Step 1.2.2

Solve the equation for $x$ .

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Step 1.2.2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$3 x + 4 = 0$

$3 x + 11 = 0$

Step 1.2.2.2

Set $3 x + 4$ equal to $0$ and solve for $x$ .

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Step 1.2.2.2.1

Set $3 x + 4$ equal to $0$ .

$3 x + 4 = 0$

Step 1.2.2.2.2

Solve $3 x + 4 = 0$ for $x$ .

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Step 1.2.2.2.2.1

Subtract $4$ from both sides of the equation.

$3 x = - 4$

Step 1.2.2.2.2.2

Divide each term in $3 x = - 4$ by $3$ and simplify.

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Step 1.2.2.2.2.2.1

Divide each term in $3 x = - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 1.2.2.2.2.2.2

Simplify the left side.

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Step 1.2.2.2.2.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.2.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 4}{3}$

Step 1.2.2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{3}$

Step 1.2.2.2.2.2.3

Simplify the right side.

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Step 1.2.2.2.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 1.2.2.3

Set $3 x + 11$ equal to $0$ and solve for $x$ .

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Step 1.2.2.3.1

Set $3 x + 11$ equal to $0$ .

$3 x + 11 = 0$

Step 1.2.2.3.2

Solve $3 x + 11 = 0$ for $x$ .

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Step 1.2.2.3.2.1

Subtract $11$ from both sides of the equation.

$3 x = - 11$

Step 1.2.2.3.2.2

Divide each term in $3 x = - 11$ by $3$ and simplify.

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Step 1.2.2.3.2.2.1

Divide each term in $3 x = - 11$ by $3$ .

$\frac{3 x}{3} = \frac{- 11}{3}$

Step 1.2.2.3.2.2.2

Simplify the left side.

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Step 1.2.2.3.2.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.3.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 11}{3}$

Step 1.2.2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 11}{3}$

Step 1.2.2.3.2.2.3

Simplify the right side.

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Step 1.2.2.3.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{11}{3}$

Step 1.2.2.4

The final solution is all the values that make $(3 x + 4) \cdot (3 x + 11) = 0$ true.

$x = - \frac{4}{3}, - \frac{11}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{4}{3}, 0), (- \frac{11}{3}, 0)$

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 $y$ .

$\frac{(3 (0) + 4) \cdot (3 (0) + 11)}{(7 (0) + 2) \cdot ((0) + 5)} = y$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $y = \frac{(3 (0) + 4) \cdot (3 (0) + 11)}{(7 (0) + 2) \cdot ((0) + 5)}$ .

$y = \frac{(3 (0) + 4) \cdot (3 (0) + 11)}{(7 (0) + 2) \cdot ((0) + 5)}$

Step 2.2.2

Simplify $\frac{(3 (0) + 4) \cdot (3 (0) + 11)}{(7 (0) + 2) \cdot ((0) + 5)}$ .

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Step 2.2.2.1

Cancel the common factor of $3 (0) + 4$ and $7 (0) + 2$ .

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Step 2.2.2.1.1

Factor $2$ out of $(3 (0) + 4) \cdot (3 (0) + 11)$ .

$y = \frac{2 ((3 \cdot (0) + 2) \cdot (3 (0) + 11))}{(7 (0) + 2) \cdot ((0) + 5)}$

Step 2.2.2.1.2

Cancel the common factors.

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Step 2.2.2.1.2.1

Factor $2$ out of $(7 (0) + 2) \cdot ((0) + 5)$ .

$y = \frac{2 ((3 \cdot (0) + 2) \cdot (3 (0) + 11))}{2 ((7 \cdot (0) + 1) \cdot ((0) + 5))}$

Step 2.2.2.1.2.2

Cancel the common factor.

$y = \frac{2 ((3 \cdot (0) + 2) \cdot (3 (0) + 11))}{2 ((7 \cdot (0) + 1) \cdot ((0) + 5))}$

Step 2.2.2.1.2.3

Rewrite the expression.

$y = \frac{(3 \cdot (0) + 2) \cdot (3 (0) + 11)}{(7 \cdot (0) + 1) \cdot ((0) + 5)}$

Step 2.2.2.2

Simplify the numerator.

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Step 2.2.2.2.1

Multiply $3$ by $0$ .

$y = \frac{(0 + 2) (3 (0) + 11)}{(7 \cdot (0) + 1) \cdot (0 + 5)}$

Step 2.2.2.2.2

Add $0$ and $2$ .

$y = \frac{2 (3 (0) + 11)}{(7 \cdot (0) + 1) \cdot (0 + 5)}$

Step 2.2.2.2.3

Multiply $3$ by $0$ .

$y = \frac{2 (0 + 11)}{(7 \cdot (0) + 1) \cdot (0 + 5)}$

Step 2.2.2.2.4

Add $0$ and $11$ .

$y = \frac{2 \cdot 11}{(7 \cdot (0) + 1) \cdot (0 + 5)}$

Step 2.2.2.3

Simplify the denominator.

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Step 2.2.2.3.1

Multiply $7$ by $0$ .

$y = \frac{2 \cdot 11}{(0 + 1) (0 + 5)}$

Step 2.2.2.3.2

Add $0$ and $1$ .

$y = \frac{2 \cdot 11}{1 (0 + 5)}$

Step 2.2.2.3.3

Multiply $0 + 5$ by $1$ .

$y = \frac{2 \cdot 11}{0 + 5}$

Step 2.2.2.3.4

Add $0$ and $5$ .

$y = \frac{2 \cdot 11}{5}$

Step 2.2.2.4

Multiply $2$ by $11$ .

$y = \frac{22}{5}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{22}{5})$

Step 3

List the intersections.

x-intercept(s): $(- \frac{4}{3}, 0), (- \frac{11}{3}, 0)$

y-intercept(s): $(0, \frac{22}{5})$

Step 4