Basic Math Examples

$| \frac{2 y - 9}{8} | = 1$

Step 1

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

$\frac{2 y - 9}{8} = \pm 1$

Step 2

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

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Step 2.1

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

$\frac{2 y - 9}{8} = 1$

Step 2.2

Multiply both sides by $8$ .

$\frac{2 y - 9}{8} \cdot 8 = 1 \cdot 8$

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of $8$ .

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Step 2.3.1.1.1

Cancel the common factor.

$\frac{2 y - 9}{8} \cdot 8 = 1 \cdot 8$

Step 2.3.1.1.2

Rewrite the expression.

$2 y - 9 = 1 \cdot 8$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $8$ by $1$ .

$2 y - 9 = 8$

Step 2.4

Solve for $y$ .

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Step 2.4.1

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

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Step 2.4.1.1

Add $9$ to both sides of the equation.

$2 y = 8 + 9$

Step 2.4.1.2

Add $8$ and $9$ .

$2 y = 17$

Step 2.4.2

Divide each term in $2 y = 17$ by $2$ and simplify.

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Step 2.4.2.1

Divide each term in $2 y = 17$ by $2$ .

$\frac{2 y}{2} = \frac{17}{2}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $2$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{17}{2}$

Step 2.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{17}{2}$

Step 2.5

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

$\frac{2 y - 9}{8} = - 1$

Step 2.6

Multiply both sides by $8$ .

$\frac{2 y - 9}{8} \cdot 8 = - 1 \cdot 8$

Step 2.7

Simplify.

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Step 2.7.1

Simplify the left side.

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Step 2.7.1.1

Cancel the common factor of $8$ .

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Step 2.7.1.1.1

Cancel the common factor.

$\frac{2 y - 9}{8} \cdot 8 = - 1 \cdot 8$

Step 2.7.1.1.2

Rewrite the expression.

$2 y - 9 = - 1 \cdot 8$

Step 2.7.2

Simplify the right side.

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Step 2.7.2.1

Multiply $- 1$ by $8$ .

$2 y - 9 = - 8$

Step 2.8

Solve for $y$ .

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Step 2.8.1

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

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Step 2.8.1.1

Add $9$ to both sides of the equation.

$2 y = - 8 + 9$

Step 2.8.1.2

Add $- 8$ and $9$ .

$2 y = 1$

Step 2.8.2

Divide each term in $2 y = 1$ by $2$ and simplify.

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Step 2.8.2.1

Divide each term in $2 y = 1$ by $2$ .

$\frac{2 y}{2} = \frac{1}{2}$

Step 2.8.2.2

Simplify the left side.

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Step 2.8.2.2.1

Cancel the common factor of $2$ .

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Step 2.8.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{1}{2}$

Step 2.8.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{2}$

Step 2.9

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

$y = \frac{17}{2}, \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{17}{2}, \frac{1}{2}$

Decimal Form:

$y = 8.5, 0.5$

Mixed Number Form:

$y = 8 \frac{1}{2}, \frac{1}{2}$