Algebra Examples

$20 = | 3 y - 11 |$

Step 1

Rewrite the equation as $| 3 y - 11 | = 20$ .

$| 3 y - 11 | = 20$

Step 2

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

$3 y - 11 = \pm 20$

Step 3

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

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Step 3.1

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

$3 y - 11 = 20$

Step 3.2

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

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Step 3.2.1

Add $11$ to both sides of the equation.

$3 y = 20 + 11$

Step 3.2.2

Add $20$ and $11$ .

$3 y = 31$

Step 3.3

Divide each term in $3 y = 31$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 y = 31$ by $3$ .

$\frac{3 y}{3} = \frac{31}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{31}{3}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{31}{3}$

Step 3.4

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

$3 y - 11 = - 20$

Step 3.5

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

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Step 3.5.1

Add $11$ to both sides of the equation.

$3 y = - 20 + 11$

Step 3.5.2

Add $- 20$ and $11$ .

$3 y = - 9$

Step 3.6

Divide each term in $3 y = - 9$ by $3$ and simplify.

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Step 3.6.1

Divide each term in $3 y = - 9$ by $3$ .

$\frac{3 y}{3} = \frac{- 9}{3}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $3$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 9}{3}$

Step 3.6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 9}{3}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $- 9$ by $3$ .

$y = - 3$

Step 3.7

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

$y = \frac{31}{3}, - 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{31}{3}, - 3$

Decimal Form:

$y = 10.\overline{3}, - 3$

Mixed Number Form:

$y = 10 \frac{1}{3}, - 3$