Algebra Examples

$q (x) = \frac{3}{10} | x |$

Step 1

Write $q (x) = \frac{3}{10} | x |$ as an equation.

$y = \frac{3}{10} | x |$

Step 2

Combine $\frac{3}{10}$ and $| x |$ .

$y = \frac{3 | x |}{10}$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Simplify $\frac{3 | 0 |}{10}$ .

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Step 4.1.1

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

$y = \frac{3 \cdot 0}{10}$

Step 4.1.2

Multiply $3$ by $0$ .

$y = \frac{0}{10}$

Step 4.1.3

Divide $0$ by $10$ .

$y = 0$

Step 4.2

Use the $x$ and $y$ values to form the ordered pair.

$(0, 0)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Simplify $\frac{3 | 1 |}{10}$ .

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Step 5.1.1

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$y = \frac{3 \cdot 1}{10}$

Step 5.1.2

Multiply $3$ by $1$ .

$y = \frac{3}{10}$

Step 5.2

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{3}{10})$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Simplify $\frac{3 | 2 |}{10}$ .

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Step 6.1.1

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$y = \frac{3 \cdot 2}{10}$

Step 6.1.2

Multiply $3$ by $2$ .

$y = \frac{6}{10}$

Step 6.1.3

Cancel the common factor of $6$ and $10$ .

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Step 6.1.3.1

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{10}$

Step 6.1.3.2

Cancel the common factors.

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Step 6.1.3.2.1

Factor $2$ out of $10$ .

$y = \frac{2 \cdot 3}{2 \cdot 5}$

Step 6.1.3.2.2

Cancel the common factor.

$y = \frac{2 \cdot 3}{2 \cdot 5}$

Step 6.1.3.2.3

Rewrite the expression.

$y = \frac{3}{5}$

Step 6.2

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{3}{5})$

Step 7

These are three possible solutions to the equation.

$(0, 0), (1, \frac{3}{10}), (2, \frac{3}{5})$

Step 8