Algebra Examples

$y = - 5 - | x - 3 |$

Step 1

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

Step 2

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

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Step 2.1

Simplify $- 5 - | (0) - 3 |$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Subtract $3$ from $0$ .

$y = - 5 - | - 3 |$

Step 2.1.1.2

The absolute value is the distance between a number and zero. The distance between $- 3$ and $0$ is $3$ .

$y = - 5 - 1 \cdot 3$

Step 2.1.1.3

Multiply $- 1$ by $3$ .

$y = - 5 - 3$

Step 2.1.2

Subtract $3$ from $- 5$ .

$y = - 8$

Step 2.2

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

$(0, - 8)$

Step 3

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

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Step 3.1

Simplify $- 5 - | (1) - 3 |$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Subtract $3$ from $1$ .

$y = - 5 - | - 2 |$

Step 3.1.1.2

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

$y = - 5 - 1 \cdot 2$

Step 3.1.1.3

Multiply $- 1$ by $2$ .

$y = - 5 - 2$

Step 3.1.2

Subtract $2$ from $- 5$ .

$y = - 7$

Step 3.2

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

$(1, - 7)$

Step 4

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

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Step 4.1

Simplify $- 5 - | (2) - 3 |$ .

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Step 4.1.1

Simplify each term.

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Step 4.1.1.1

Subtract $3$ from $2$ .

$y = - 5 - | - 1 |$

Step 4.1.1.2

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

$y = - 5 - 1 \cdot 1$

Step 4.1.1.3

Multiply $- 1$ by $1$ .

$y = - 5 - 1$

Step 4.1.2

Subtract $1$ from $- 5$ .

$y = - 6$

Step 4.2

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

$(2, - 6)$

Step 5

These are three possible solutions to the equation.

$(0, - 8), (1, - 7), (2, - 6)$

Step 6