Basic Math Examples

$\frac{1}{2} \cdot | y - 9 | = 16$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot | y - 9 |) = 2 \cdot 16$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 (\frac{1}{2} \cdot | y - 9 |)$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $| y - 9 |$ .

$2 \frac{| y - 9 |}{2} = 2 \cdot 16$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{| y - 9 |}{2} = 2 \cdot 16$

Step 2.1.1.2.2

Rewrite the expression.

$| y - 9 | = 2 \cdot 16$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $16$ .

$| y - 9 | = 32$

Step 3

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

$y - 9 = \pm 32$

Step 4

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

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Step 4.1

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

$y - 9 = 32$

Step 4.2

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

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Step 4.2.1

Add $9$ to both sides of the equation.

$y = 32 + 9$

Step 4.2.2

Add $32$ and $9$ .

$y = 41$

Step 4.3

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

$y - 9 = - 32$

Step 4.4

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

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Step 4.4.1

Add $9$ to both sides of the equation.

$y = - 32 + 9$

Step 4.4.2

Add $- 32$ and $9$ .

$y = - 23$

Step 4.5

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

$y = 41, - 23$