Precalculus Examples

$3 (x - 2) + y = 7 - 6 (y + 4)$

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 $x$ .

$3 (x - 2) + 0 = 7 - 6 ((0) + 4)$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $3 (x - 2) + 0$ .

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Step 1.2.1.1

Add $3 (x - 2)$ and $0$ .

$3 (x - 2) = 7 - 6 ((0) + 4)$

Step 1.2.1.2

Apply the distributive property.

$3 x + 3 \cdot - 2 = 7 - 6 ((0) + 4)$

Step 1.2.1.3

Multiply $3$ by $- 2$ .

$3 x - 6 = 7 - 6 ((0) + 4)$

Step 1.2.2

Simplify $7 - 6 ((0) + 4)$ .

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Step 1.2.2.1

Simplify each term.

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Step 1.2.2.1.1

Add $0$ and $4$ .

$3 x - 6 = 7 - 6 \cdot 4$

Step 1.2.2.1.2

Multiply $- 6$ by $4$ .

$3 x - 6 = 7 - 24$

Step 1.2.2.2

Subtract $24$ from $7$ .

$3 x - 6 = - 17$

Step 1.2.3

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

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Step 1.2.3.1

Add $6$ to both sides of the equation.

$3 x = - 17 + 6$

Step 1.2.3.2

Add $- 17$ and $6$ .

$3 x = - 11$

Step 1.2.4

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

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Step 1.2.4.1

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

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

Step 1.2.4.2

Simplify the left side.

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Step 1.2.4.2.1

Cancel the common factor of $3$ .

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Step 1.2.4.2.1.1

Cancel the common factor.

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

Step 1.2.4.2.1.2

Divide $x$ by $1$ .

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

Step 1.2.4.3

Simplify the right side.

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Step 1.2.4.3.1

Move the negative in front of the fraction.

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

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$3 ((0) - 2) + y = 7 - 6 (y + 4)$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $3 ((0) - 2) + y$ .

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Step 2.2.1.1

Subtract $2$ from $0$ .

$3 \cdot - 2 + y = 7 - 6 (y + 4)$

Step 2.2.1.2

Multiply $3$ by $- 2$ .

$- 6 + y = 7 - 6 (y + 4)$

Step 2.2.2

Simplify $7 - 6 (y + 4)$ .

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Step 2.2.2.1

Simplify each term.

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Step 2.2.2.1.1

Apply the distributive property.

$- 6 + y = 7 - 6 y - 6 \cdot 4$

Step 2.2.2.1.2

Multiply $- 6$ by $4$ .

$- 6 + y = 7 - 6 y - 24$

Step 2.2.2.2

Subtract $24$ from $7$ .

$- 6 + y = - 6 y - 17$

Step 2.2.3

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

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Step 2.2.3.1

Add $6 y$ to both sides of the equation.

$- 6 + y + 6 y = - 17$

Step 2.2.3.2

Add $y$ and $6 y$ .

$- 6 + 7 y = - 17$

Step 2.2.4

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

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Step 2.2.4.1

Add $6$ to both sides of the equation.

$7 y = - 17 + 6$

Step 2.2.4.2

Add $- 17$ and $6$ .

$7 y = - 11$

Step 2.2.5

Divide each term in $7 y = - 11$ by $7$ and simplify.

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Step 2.2.5.1

Divide each term in $7 y = - 11$ by $7$ .

$\frac{7 y}{7} = \frac{- 11}{7}$

Step 2.2.5.2

Simplify the left side.

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Step 2.2.5.2.1

Cancel the common factor of $7$ .

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Step 2.2.5.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 11}{7}$

Step 2.2.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 11}{7}$

Step 2.2.5.3

Simplify the right side.

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Step 2.2.5.3.1

Move the negative in front of the fraction.

$y = - \frac{11}{7}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{11}{7})$

Step 3

List the intersections.

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

y-intercept(s): $(0, - \frac{11}{7})$

Step 4