Algebra Examples

$y = - 2 | x - 4 | + 8$

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 $x$ .

$0 = - 2 | x - 4 | + 8$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- 2 | x - 4 | + 8 = 0$ .

$- 2 | x - 4 | + 8 = 0$

Step 1.2.2

Subtract $8$ from both sides of the equation.

$- 2 | x - 4 | = - 8$

Step 1.2.3

Divide each term in $- 2 | x - 4 | = - 8$ by $- 2$ and simplify.

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Step 1.2.3.1

Divide each term in $- 2 | x - 4 | = - 8$ by $- 2$ .

$\frac{- 2 | x - 4 |}{- 2} = \frac{- 8}{- 2}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{- 2 | x - 4 |}{- 2} = \frac{- 8}{- 2}$

Step 1.2.3.2.1.2

Divide $| x - 4 |$ by $1$ .

$| x - 4 | = \frac{- 8}{- 2}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 8$ by $- 2$ .

$| x - 4 | = 4$

Step 1.2.4

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x - 4 = \pm 4$

Step 1.2.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 1.2.5.1

First, use the positive value of the $\pm$ to find the first solution.

$x - 4 = 4$

Step 1.2.5.2

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

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Step 1.2.5.2.1

Add $4$ to both sides of the equation.

$x = 4 + 4$

Step 1.2.5.2.2

Add $4$ and $4$ .

$x = 8$

Step 1.2.5.3

Next, use the negative value of the $\pm$ to find the second solution.

$x - 4 = - 4$

Step 1.2.5.4

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

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Step 1.2.5.4.1

Add $4$ to both sides of the equation.

$x = - 4 + 4$

Step 1.2.5.4.2

Add $- 4$ and $4$ .

$x = 0$

Step 1.2.5.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = 8, 0$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(8, 0), (0, 0)$

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 $y$ .

$y = - 2 | (0) - 4 | + 8$

Step 2.2

Simplify $- 2 | (0) - 4 | + 8$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Subtract $4$ from $0$ .

$y = - 2 | - 4 | + 8$

Step 2.2.1.2

The absolute value is the distance between a number and zero. The distance between $- 4$ and $0$ is $4$ .

$y = - 2 \cdot 4 + 8$

Step 2.2.1.3

Multiply $- 2$ by $4$ .

$y = - 8 + 8$

Step 2.2.2

Add $- 8$ and $8$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(8, 0), (0, 0)$

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

Step 4