Basic Math Examples

$9 (4 y - 3) - 12 y = 4 (27 + 5 y)$

Step 1

Simplify $9 (4 y - 3) - 12 y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$9 (4 y) + 9 \cdot - 3 - 12 y = 4 (27 + 5 y)$

Step 1.1.2

Multiply $4$ by $9$ .

$36 y + 9 \cdot - 3 - 12 y = 4 (27 + 5 y)$

Step 1.1.3

Multiply $9$ by $- 3$ .

$36 y - 27 - 12 y = 4 (27 + 5 y)$

Step 1.2

Subtract $12 y$ from $36 y$ .

$24 y - 27 = 4 (27 + 5 y)$

Step 2

Simplify $4 (27 + 5 y)$ .

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Step 2.1

Apply the distributive property.

$24 y - 27 = 4 \cdot 27 + 4 (5 y)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $4$ by $27$ .

$24 y - 27 = 108 + 4 (5 y)$

Step 2.2.2

Multiply $5$ by $4$ .

$24 y - 27 = 108 + 20 y$

Step 3

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

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Step 3.1

Subtract $20 y$ from both sides of the equation.

$24 y - 27 - 20 y = 108$

Step 3.2

Subtract $20 y$ from $24 y$ .

$4 y - 27 = 108$

Step 4

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

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Step 4.1

Add $27$ to both sides of the equation.

$4 y = 108 + 27$

Step 4.2

Add $108$ and $27$ .

$4 y = 135$

Step 5

Divide each term in $4 y = 135$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 y = 135$ by $4$ .

$\frac{4 y}{4} = \frac{135}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{135}{4}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{135}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{135}{4}$

Decimal Form:

$y = 33.75$

Mixed Number Form:

$y = 33 \frac{3}{4}$