Basic Math Examples

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

Step 1

Cancel the common factor of $6$ and $3$ .

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Step 1.1

Factor $3$ out of $6 (y + 2)$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 (y + 2))}{3 (1)} = 4 y - 3$

Step 1.2.2

Cancel the common factor.

$\frac{3 (2 (y + 2))}{3 \cdot 1} = 4 y - 3$

Step 1.2.3

Rewrite the expression.

$\frac{2 (y + 2)}{1} = 4 y - 3$

Step 1.2.4

Divide $2 (y + 2)$ by $1$ .

$2 (y + 2) = 4 y - 3$

Step 2

Solve for $y$ .

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Step 2.1

Simplify $2 (y + 2)$ .

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Step 2.1.1

Rewrite.

$0 + 0 + 2 (y + 2) = 4 y - 3$

Step 2.1.2

Simplify by adding zeros.

$2 (y + 2) = 4 y - 3$

Step 2.1.3

Apply the distributive property.

$2 y + 2 \cdot 2 = 4 y - 3$

Step 2.1.4

Multiply $2$ by $2$ .

$2 y + 4 = 4 y - 3$

Step 2.2

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

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Step 2.2.1

Subtract $4 y$ from both sides of the equation.

$2 y + 4 - 4 y = - 3$

Step 2.2.2

Subtract $4 y$ from $2 y$ .

$- 2 y + 4 = - 3$

Step 2.3

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

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Step 2.3.1

Subtract $4$ from both sides of the equation.

$- 2 y = - 3 - 4$

Step 2.3.2

Subtract $4$ from $- 3$ .

$- 2 y = - 7$

Step 2.4

Divide each term in $- 2 y = - 7$ by $- 2$ and simplify.

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Step 2.4.1

Divide each term in $- 2 y = - 7$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 7}{- 2}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 2$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 7}{- 2}$

Step 2.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7}{- 2}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Dividing two negative values results in a positive value.

$y = \frac{7}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{2}$

Decimal Form:

$y = 3.5$

Mixed Number Form:

$y = 3 \frac{1}{2}$