Basic Math Examples

$\frac{2 y - 5}{14} = \frac{z - 3}{9}$

Step 1

Multiply both sides by $14$ .

$\frac{2 y - 5}{14} \cdot 14 = \frac{z - 3}{9} \cdot 14$

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 $14$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{2 y - 5}{14} \cdot 14 = \frac{z - 3}{9} \cdot 14$

Step 2.1.1.2

Rewrite the expression.

$2 y - 5 = \frac{z - 3}{9} \cdot 14$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{z - 3}{9} \cdot 14$ .

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Step 2.2.1.1

Combine $\frac{z - 3}{9}$ and $14$ .

$2 y - 5 = \frac{(z - 3) \cdot 14}{9}$

Step 2.2.1.2

Move $14$ to the left of $z - 3$ .

$2 y - 5 = \frac{14 (z - 3)}{9}$

Step 3

Solve for $y$ .

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Step 3.1

Add $5$ to both sides of the equation.

$2 y = \frac{14 (z - 3)}{9} + 5$

Step 3.2

Divide each term in $2 y = \frac{14 (z - 3)}{9} + 5$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 y = \frac{14 (z - 3)}{9} + 5$ by $2$ .

$\frac{2 y}{2} = \frac{\frac{14 (z - 3)}{9}}{2} + \frac{5}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{\frac{14 (z - 3)}{9}}{2} + \frac{5}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{14 (z - 3)}{9}}{2} + \frac{5}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Combine the numerators over the common denominator.

$y = \frac{\frac{14 (z - 3)}{9} + 5}{2}$

Step 3.2.3.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{\frac{14 (z - 3)}{9} + 5 \cdot \frac{9}{9}}{2}$

Step 3.2.3.3

Simplify terms.

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Step 3.2.3.3.1

Combine $5$ and $\frac{9}{9}$ .

$y = \frac{\frac{14 (z - 3)}{9} + \frac{5 \cdot 9}{9}}{2}$

Step 3.2.3.3.2

Combine the numerators over the common denominator.

$y = \frac{\frac{14 (z - 3) + 5 \cdot 9}{9}}{2}$

Step 3.2.3.4

Simplify the numerator.

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Step 3.2.3.4.1

Apply the distributive property.

$y = \frac{\frac{14 z + 14 \cdot - 3 + 5 \cdot 9}{9}}{2}$

Step 3.2.3.4.2

Multiply $14$ by $- 3$ .

$y = \frac{\frac{14 z - 42 + 5 \cdot 9}{9}}{2}$

Step 3.2.3.4.3

Multiply $5$ by $9$ .

$y = \frac{\frac{14 z - 42 + 45}{9}}{2}$

Step 3.2.3.4.4

Add $- 42$ and $45$ .

$y = \frac{\frac{14 z + 3}{9}}{2}$

Step 3.2.3.5

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{14 z + 3}{9} \cdot \frac{1}{2}$

Step 3.2.3.6

Multiply $\frac{14 z + 3}{9} \cdot \frac{1}{2}$ .

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Step 3.2.3.6.1

Multiply $\frac{14 z + 3}{9}$ by $\frac{1}{2}$ .

$y = \frac{14 z + 3}{9 \cdot 2}$

Step 3.2.3.6.2

Multiply $9$ by $2$ .

$y = \frac{14 z + 3}{18}$