Basic Math Examples

$\frac{4 y + 5}{2} = y + 9$

Step 1

Multiply both sides by $2$ .

$\frac{4 y + 5}{2} \cdot 2 = (y + 9) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{4 y + 5}{2} \cdot 2 = (y + 9) \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$4 y + 5 = (y + 9) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(y + 9) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$4 y + 5 = y \cdot 2 + 9 \cdot 2$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $2$ to the left of $y$ .

$4 y + 5 = 2 \cdot y + 9 \cdot 2$

Step 2.2.1.2.2

Multiply $9$ by $2$ .

$4 y + 5 = 2 y + 18$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Subtract $2 y$ from both sides of the equation.

$4 y + 5 - 2 y = 18$

Step 3.1.2

Subtract $2 y$ from $4 y$ .

$2 y + 5 = 18$

Step 3.2

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

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Step 3.2.1

Subtract $5$ from both sides of the equation.

$2 y = 18 - 5$

Step 3.2.2

Subtract $5$ from $18$ .

$2 y = 13$

Step 3.3

Divide each term in $2 y = 13$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 y = 13$ by $2$ .

$\frac{2 y}{2} = \frac{13}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{13}{2}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{13}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{13}{2}$

Decimal Form:

$y = 6.5$

Mixed Number Form:

$y = 6 \frac{1}{2}$