Basic Math Examples

$3 - | y + 9 | = 11 - 3 | y + 9 |$

Step 1

Move all terms containing $| y + 9 |$ to the left side of the equation.

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Step 1.1

Add $3 | y + 9 |$ to both sides of the equation.

$3 - | y + 9 | + 3 | y + 9 | = 11$

Step 1.2

Add $- | y + 9 |$ and $3 | y + 9 |$ .

$3 + 2 | y + 9 | = 11$

Step 2

Move all terms not containing $| y + 9 |$ to the right side of the equation.

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Step 2.1

Subtract $3$ from both sides of the equation.

$2 | y + 9 | = 11 - 3$

Step 2.2

Subtract $3$ from $11$ .

$2 | y + 9 | = 8$

Step 3

Divide each term in $2 | y + 9 | = 8$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 | y + 9 | = 8$ by $2$ .

$\frac{2 | y + 9 |}{2} = \frac{8}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 | y + 9 |}{2} = \frac{8}{2}$

Step 3.2.1.2

Divide $| y + 9 |$ by $1$ .

$| y + 9 | = \frac{8}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $8$ by $2$ .

$| y + 9 | = 4$

Step 4

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

$y + 9 = \pm 4$

Step 5

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

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Step 5.1

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

$y + 9 = 4$

Step 5.2

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

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Step 5.2.1

Subtract $9$ from both sides of the equation.

$y = 4 - 9$

Step 5.2.2

Subtract $9$ from $4$ .

$y = - 5$

Step 5.3

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

$y + 9 = - 4$

Step 5.4

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

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Step 5.4.1

Subtract $9$ from both sides of the equation.

$y = - 4 - 9$

Step 5.4.2

Subtract $9$ from $- 4$ .

$y = - 13$

Step 5.5

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

$y = - 5, - 13$

Step 6