Basic Math Examples

$\frac{2 y - 1}{5} - \frac{y + 3}{7} = 0$

Step 1

Simplify $\frac{2 y - 1}{5} - \frac{y + 3}{7}$ .

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Step 1.1

To write $\frac{2 y - 1}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2 y - 1}{5} \cdot \frac{7}{7} - \frac{y + 3}{7} = 0$

Step 1.2

To write $- \frac{y + 3}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 y - 1}{5} \cdot \frac{7}{7} - \frac{y + 3}{7} \cdot \frac{5}{5} = 0$

Step 1.3

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{2 y - 1}{5}$ by $\frac{7}{7}$ .

$\frac{(2 y - 1) \cdot 7}{5 \cdot 7} - \frac{y + 3}{7} \cdot \frac{5}{5} = 0$

Step 1.3.2

Multiply $5$ by $7$ .

$\frac{(2 y - 1) \cdot 7}{35} - \frac{y + 3}{7} \cdot \frac{5}{5} = 0$

Step 1.3.3

Multiply $\frac{y + 3}{7}$ by $\frac{5}{5}$ .

$\frac{(2 y - 1) \cdot 7}{35} - \frac{(y + 3) \cdot 5}{7 \cdot 5} = 0$

Step 1.3.4

Multiply $7$ by $5$ .

$\frac{(2 y - 1) \cdot 7}{35} - \frac{(y + 3) \cdot 5}{35} = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(2 y - 1) \cdot 7 - (y + 3) \cdot 5}{35} = 0$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{2 y \cdot 7 - 1 \cdot 7 - (y + 3) \cdot 5}{35} = 0$

Step 1.5.2

Multiply $7$ by $2$ .

$\frac{14 y - 1 \cdot 7 - (y + 3) \cdot 5}{35} = 0$

Step 1.5.3

Multiply $- 1$ by $7$ .

$\frac{14 y - 7 - (y + 3) \cdot 5}{35} = 0$

Step 1.5.4

Apply the distributive property.

$\frac{14 y - 7 + (- y - 1 \cdot 3) \cdot 5}{35} = 0$

Step 1.5.5

Multiply $- 1$ by $3$ .

$\frac{14 y - 7 + (- y - 3) \cdot 5}{35} = 0$

Step 1.5.6

Apply the distributive property.

$\frac{14 y - 7 - y \cdot 5 - 3 \cdot 5}{35} = 0$

Step 1.5.7

Multiply $5$ by $- 1$ .

$\frac{14 y - 7 - 5 y - 3 \cdot 5}{35} = 0$

Step 1.5.8

Multiply $- 3$ by $5$ .

$\frac{14 y - 7 - 5 y - 15}{35} = 0$

Step 1.5.9

Subtract $5 y$ from $14 y$ .

$\frac{9 y - 7 - 15}{35} = 0$

Step 1.5.10

Subtract $15$ from $- 7$ .

$\frac{9 y - 22}{35} = 0$

Step 2

Set the numerator equal to zero.

$9 y - 22 = 0$

Step 3

Solve the equation for $y$ .

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Step 3.1

Add $22$ to both sides of the equation.

$9 y = 22$

Step 3.2

Divide each term in $9 y = 22$ by $9$ and simplify.

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Step 3.2.1

Divide each term in $9 y = 22$ by $9$ .

$\frac{9 y}{9} = \frac{22}{9}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $9$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{22}{9}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{22}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{22}{9}$

Decimal Form:

$y = 2.\overline{4}$

Mixed Number Form:

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