Algebra Examples

$y = | x - 1 | + 3$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = | (- 2) - 1 | + 3$

Step 2

Simplify $| (- 2) - 1 | + 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Subtract $1$ from $- 2$ .

$y = | - 3 | + 3$

Step 2.1.2

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

$y = 3 + 3$

Step 2.2

Add $3$ and $3$ .

$y = 6$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = | (- 1) - 1 | + 3$

Step 4

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

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Step 4.1

Simplify each term.

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Step 4.1.1

Subtract $1$ from $- 1$ .

$y = | - 2 | + 3$

Step 4.1.2

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

$y = 2 + 3$

Step 4.2

Add $2$ and $3$ .

$y = 5$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = | (0) - 1 | + 3$

Step 6

Simplify $| (0) - 1 | + 3$ .

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Step 6.1

Simplify each term.

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Step 6.1.1

Subtract $1$ from $0$ .

$y = | - 1 | + 3$

Step 6.1.2

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

$y = 1 + 3$

Step 6.2

Add $1$ and $3$ .

$y = 4$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = | (1) - 1 | + 3$

Step 8

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

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Step 8.1

Simplify each term.

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Step 8.1.1

Subtract $1$ from $1$ .

$y = | 0 | + 3$

Step 8.1.2

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

$y = 0 + 3$

Step 8.2

Add $0$ and $3$ .

$y = 3$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = | (2) - 1 | + 3$

Step 10

Simplify $| (2) - 1 | + 3$ .

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Step 10.1

Simplify each term.

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Step 10.1.1

Subtract $1$ from $2$ .

$y = | 1 | + 3$

Step 10.1.2

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

$y = 1 + 3$

Step 10.2

Add $1$ and $3$ .

$y = 4$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 6 \\ - 1 & 5 \\ 0 & 4 \\ 1 & 3 \\ 2 & 4 \end{array}$

Step 12