Algebra Examples

$y = 2 \sqrt[3]{x - 3} + 1$

Step 1

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

$y = 2 \sqrt[3]{(- 2) - 3} + 1$

Step 2

Simplify each term.

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Step 2.1

Subtract $3$ from $- 2$ .

$y = 2 \sqrt[3]{- 5} + 1$

Step 2.2

Rewrite $- 5$ as ${(- 1)}^{3} \cdot 5$ .

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Step 2.2.1

Rewrite $- 5$ as $- 1 (5)$ .

$y = 2 \sqrt[3]{- 1 (5)} + 1$

Step 2.2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = 2 \sqrt[3]{{(- 1)}^{3} \cdot 5} + 1$

Step 2.3

Pull terms out from under the radical.

$y = 2 (- 1 \sqrt[3]{5}) + 1$

Step 2.4

Rewrite $- 1 \sqrt[3]{5}$ as $- \sqrt[3]{5}$ .

$y = 2 (- \sqrt[3]{5}) + 1$

Step 2.5

Multiply $- 1$ by $2$ .

$y = - 2 \sqrt[3]{5} + 1$

Step 3

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

$y = 2 \sqrt[3]{(- 1) - 3} + 1$

Step 4

Simplify each term.

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Step 4.1

Subtract $3$ from $- 1$ .

$y = 2 \sqrt[3]{- 4} + 1$

Step 4.2

Rewrite $- 4$ as ${(- 1)}^{3} \cdot 4$ .

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Step 4.2.1

Rewrite $- 4$ as $- 1 (4)$ .

$y = 2 \sqrt[3]{- 1 (4)} + 1$

Step 4.2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = 2 \sqrt[3]{{(- 1)}^{3} \cdot 4} + 1$

Step 4.3

Pull terms out from under the radical.

$y = 2 (- 1 \sqrt[3]{4}) + 1$

Step 4.4

Rewrite $- 1 \sqrt[3]{4}$ as $- \sqrt[3]{4}$ .

$y = 2 (- \sqrt[3]{4}) + 1$

Step 4.5

Multiply $- 1$ by $2$ .

$y = - 2 \sqrt[3]{4} + 1$

Step 5

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

$y = 2 \sqrt[3]{(0) - 3} + 1$

Step 6

Simplify each term.

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Step 6.1

Subtract $3$ from $0$ .

$y = 2 \sqrt[3]{- 3} + 1$

Step 6.2

Rewrite $- 3$ as ${(- 1)}^{3} \cdot 3$ .

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Step 6.2.1

Rewrite $- 3$ as $- 1 (3)$ .

$y = 2 \sqrt[3]{- 1 (3)} + 1$

Step 6.2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = 2 \sqrt[3]{{(- 1)}^{3} \cdot 3} + 1$

Step 6.3

Pull terms out from under the radical.

$y = 2 (- 1 \sqrt[3]{3}) + 1$

Step 6.4

Rewrite $- 1 \sqrt[3]{3}$ as $- \sqrt[3]{3}$ .

$y = 2 (- \sqrt[3]{3}) + 1$

Step 6.5

Multiply $- 1$ by $2$ .

$y = - 2 \sqrt[3]{3} + 1$

Step 7

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

$y = 2 \sqrt[3]{(1) - 3} + 1$

Step 8

Simplify each term.

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Step 8.1

Subtract $3$ from $1$ .

$y = 2 \sqrt[3]{- 2} + 1$

Step 8.2

Rewrite $- 2$ as ${(- 1)}^{3} \cdot 2$ .

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Step 8.2.1

Rewrite $- 2$ as $- 1 (2)$ .

$y = 2 \sqrt[3]{- 1 (2)} + 1$

Step 8.2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = 2 \sqrt[3]{{(- 1)}^{3} \cdot 2} + 1$

Step 8.3

Pull terms out from under the radical.

$y = 2 (- 1 \sqrt[3]{2}) + 1$

Step 8.4

Rewrite $- 1 \sqrt[3]{2}$ as $- \sqrt[3]{2}$ .

$y = 2 (- \sqrt[3]{2}) + 1$

Step 8.5

Multiply $- 1$ by $2$ .

$y = - 2 \sqrt[3]{2} + 1$

Step 9

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

$y = 2 \sqrt[3]{(2) - 3} + 1$

Step 10

Simplify $2 \sqrt[3]{(2) - 3} + 1$ .

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Step 10.1

Simplify each term.

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Step 10.1.1

Subtract $3$ from $2$ .

$y = 2 \sqrt[3]{- 1} + 1$

Step 10.1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = 2 \sqrt[3]{{(- 1)}^{3}} + 1$

Step 10.1.3

Pull terms out from under the radical, assuming real numbers.

$y = 2 \cdot - 1 + 1$

Step 10.1.4

Multiply $2$ by $- 1$ .

$y = - 2 + 1$

Step 10.2

Add $- 2$ and $1$ .

$y = - 1$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 2 \sqrt[3]{5} + 1 \\ - 1 & - 2 \sqrt[3]{4} + 1 \\ 0 & - 2 \sqrt[3]{3} + 1 \\ 1 & - 2 \sqrt[3]{2} + 1 \\ 2 & - 1 \end{array}$

Step 12