Algebra Examples

$\frac{3}{2} = \frac{1}{6} (12 y - 24)$

Step 1

Rewrite the equation as $\frac{1}{6} \cdot (12 y - 24) = \frac{3}{2}$ .

$\frac{1}{6} \cdot (12 y - 24) = \frac{3}{2}$

Step 2

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} \cdot (12 y - 24)) = 6 (\frac{3}{2})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $6 (\frac{1}{6} \cdot (12 y - 24))$ .

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Step 3.1.1.1

Apply the distributive property.

$6 (\frac{1}{6} (12 y) + \frac{1}{6} \cdot - 24) = 6 (\frac{3}{2})$

Step 3.1.1.2

Cancel the common factor of $6$ .

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Step 3.1.1.2.1

Factor $6$ out of $12 y$ .

$6 (\frac{1}{6} (6 (2 y)) + \frac{1}{6} \cdot - 24) = 6 (\frac{3}{2})$

Step 3.1.1.2.2

Cancel the common factor.

$6 (\frac{1}{6} (6 (2 y)) + \frac{1}{6} \cdot - 24) = 6 (\frac{3}{2})$

Step 3.1.1.2.3

Rewrite the expression.

$6 (2 y + \frac{1}{6} \cdot - 24) = 6 (\frac{3}{2})$

Step 3.1.1.3

Cancel the common factor of $6$ .

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Step 3.1.1.3.1

Factor $6$ out of $- 24$ .

$6 (2 y + \frac{1}{6} \cdot (6 (- 4))) = 6 (\frac{3}{2})$

Step 3.1.1.3.2

Cancel the common factor.

$6 (2 y + \frac{1}{6} \cdot (6 \cdot - 4)) = 6 (\frac{3}{2})$

Step 3.1.1.3.3

Rewrite the expression.

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

Step 3.1.1.4

Apply the distributive property.

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

Step 3.1.1.5

Multiply.

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Step 3.1.1.5.1

Multiply $2$ by $6$ .

$12 y + 6 \cdot - 4 = 6 (\frac{3}{2})$

Step 3.1.1.5.2

Multiply $6$ by $- 4$ .

$12 y - 24 = 6 (\frac{3}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $6 (\frac{3}{2})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $6$ .

$12 y - 24 = 2 (3) \frac{3}{2}$

Step 3.2.1.1.2

Cancel the common factor.

$12 y - 24 = 2 \cdot 3 \frac{3}{2}$

Step 3.2.1.1.3

Rewrite the expression.

$12 y - 24 = 3 \cdot 3$

Step 3.2.1.2

Multiply $3$ by $3$ .

$12 y - 24 = 9$

Step 4

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

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Step 4.1

Add $24$ to both sides of the equation.

$12 y = 9 + 24$

Step 4.2

Add $9$ and $24$ .

$12 y = 33$

Step 5

Divide each term in $12 y = 33$ by $12$ and simplify.

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Step 5.1

Divide each term in $12 y = 33$ by $12$ .

$\frac{12 y}{12} = \frac{33}{12}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $12$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{33}{12}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{33}{12}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $33$ and $12$ .

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Step 5.3.1.1

Factor $3$ out of $33$ .

$y = \frac{3 (11)}{12}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $3$ out of $12$ .

$y = \frac{3 \cdot 11}{3 \cdot 4}$

Step 5.3.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot 11}{3 \cdot 4}$

Step 5.3.1.2.3

Rewrite the expression.

$y = \frac{11}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{11}{4}$

Decimal Form:

$y = 2.75$

Mixed Number Form:

$y = 2 \frac{3}{4}$