Basic Math Examples

$| 4 y | - 9 = 23$

Step 1

Move all terms not containing $| 4 y |$ to the right side of the equation.

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Step 1.1

Add $9$ to both sides of the equation.

$| 4 y | = 23 + 9$

Step 1.2

Add $23$ and $9$ .

$| 4 y | = 32$

Step 2

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

$4 y = \pm 32$

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.

$4 y = 32$

Step 3.2

Divide each term in $4 y = 32$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 y = 32$ by $4$ .

$\frac{4 y}{4} = \frac{32}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{32}{4}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{32}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $32$ by $4$ .

$y = 8$

Step 3.3

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

$4 y = - 32$

Step 3.4

Divide each term in $4 y = - 32$ by $4$ and simplify.

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Step 3.4.1

Divide each term in $4 y = - 32$ by $4$ .

$\frac{4 y}{4} = \frac{- 32}{4}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $4$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 32}{4}$

Step 3.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 32}{4}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $- 32$ by $4$ .

$y = - 8$

Step 3.5

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

$y = 8, - 8$