Basic Math Examples

$2 y - \frac{7}{6} + \frac{y}{6} = \frac{4 y + 3}{6}$

Step 1

Multiply both sides by $6$ .

$(2 y - \frac{7}{6} + \frac{y}{6}) \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(2 y - \frac{7}{6} + \frac{y}{6}) \cdot 6$ .

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Step 2.1.1.1

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(2 y \cdot \frac{6}{6} + \frac{y}{6} - \frac{7}{6}) \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2.1.1.2

Combine $2 y$ and $\frac{6}{6}$ .

$(\frac{2 y \cdot 6}{6} + \frac{y}{6} - \frac{7}{6}) \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2.1.1.3

Combine the numerators over the common denominator.

$(\frac{2 y \cdot 6 + y}{6} - \frac{7}{6}) \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{2 y \cdot 6 + y - 7}{6} \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2.1.1.5

Multiply $6$ by $2$ .

$\frac{12 y + y - 7}{6} \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2.1.1.6

Add $12 y$ and $y$ .

$\frac{13 y - 7}{6} \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2.1.1.7

Cancel the common factor of $6$ .

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Step 2.1.1.7.1

Cancel the common factor.

$\frac{13 y - 7}{6} \cdot 6 = \frac{4 y + 3}{6} \cdot 6$

Step 2.1.1.7.2

Rewrite the expression.

$13 y - 7 = \frac{4 y + 3}{6} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$13 y - 7 = \frac{4 y + 3}{6} \cdot 6$

Step 2.2.1.2

Rewrite the expression.

$13 y - 7 = 4 y + 3$

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 $4 y$ from both sides of the equation.

$13 y - 7 - 4 y = 3$

Step 3.1.2

Subtract $4 y$ from $13 y$ .

$9 y - 7 = 3$

Step 3.2

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

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Step 3.2.1

Add $7$ to both sides of the equation.

$9 y = 3 + 7$

Step 3.2.2

Add $3$ and $7$ .

$9 y = 10$

Step 3.3

Divide each term in $9 y = 10$ by $9$ and simplify.

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Step 3.3.1

Divide each term in $9 y = 10$ by $9$ .

$\frac{9 y}{9} = \frac{10}{9}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $9$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{10}{9}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{10}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{10}{9}$

Decimal Form:

$y = 1.\overline{1}$

Mixed Number Form:

$y = 1 \frac{1}{9}$