Algebra Examples

$5 (x - 2) = 12 - y$

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 $x$ .

$5 (x - 2) = 12 - (0)$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify.

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Step 1.2.1.1

Multiply $- 1$ by $0$ .

$5 (x - 2) = 12 + 0$

Step 1.2.1.2

Add $12$ and $0$ .

$5 (x - 2) = 12$

Step 1.2.2

Divide each term in $5 (x - 2) = 12$ by $5$ and simplify.

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Step 1.2.2.1

Divide each term in $5 (x - 2) = 12$ by $5$ .

$\frac{5 (x - 2)}{5} = \frac{12}{5}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{5 (x - 2)}{5} = \frac{12}{5}$

Step 1.2.2.2.1.2

Divide $x - 2$ by $1$ .

$x - 2 = \frac{12}{5}$

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 $2$ to both sides of the equation.

$x = \frac{12}{5} + 2$

Step 1.2.3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \frac{12}{5} + 2 \cdot \frac{5}{5}$

Step 1.2.3.3

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

$x = \frac{12}{5} + \frac{2 \cdot 5}{5}$

Step 1.2.3.4

Combine the numerators over the common denominator.

$x = \frac{12 + 2 \cdot 5}{5}$

Step 1.2.3.5

Simplify the numerator.

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Step 1.2.3.5.1

Multiply $2$ by $5$ .

$x = \frac{12 + 10}{5}$

Step 1.2.3.5.2

Add $12$ and $10$ .

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

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$5 ((0) - 2) = 12 - y$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $12 - y = 5 ((0) - 2)$ .

$12 - y = 5 ((0) - 2)$

Step 2.2.2

Simplify $5 ((0) - 2)$ .

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Step 2.2.2.1

Subtract $2$ from $0$ .

$12 - y = 5 \cdot - 2$

Step 2.2.2.2

Multiply $5$ by $- 2$ .

$12 - y = - 10$

Step 2.2.3

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

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Step 2.2.3.1

Subtract $12$ from both sides of the equation.

$- y = - 10 - 12$

Step 2.2.3.2

Subtract $12$ from $- 10$ .

$- y = - 22$

Step 2.2.4

Divide each term in $- y = - 22$ by $- 1$ and simplify.

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Step 2.2.4.1

Divide each term in $- y = - 22$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 22}{- 1}$

Step 2.2.4.2

Simplify the left side.

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Step 2.2.4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 22}{- 1}$

Step 2.2.4.2.2

Divide $y$ by $1$ .

$y = \frac{- 22}{- 1}$

Step 2.2.4.3

Simplify the right side.

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Step 2.2.4.3.1

Divide $- 22$ by $- 1$ .

$y = 22$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 22)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 22)$

Step 4