Pre-Algebra Examples

$\frac{2}{3} \cdot (6 t + 12) = 28$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (6 t + 12)) = \frac{3}{2} \cdot 28$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (6 t + 12))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} (6 t) + \frac{2}{3} \cdot 12) = \frac{3}{2} \cdot 28$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $6 t$ .

$\frac{3}{2} (\frac{2}{3} (3 (2 t)) + \frac{2}{3} \cdot 12) = \frac{3}{2} \cdot 28$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{3}{2} (\frac{2}{3} (3 (2 t)) + \frac{2}{3} \cdot 12) = \frac{3}{2} \cdot 28$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{3}{2} (2 (2 t) + \frac{2}{3} \cdot 12) = \frac{3}{2} \cdot 28$

Step 2.1.1.3

Multiply $2$ by $2$ .

$\frac{3}{2} (4 t + \frac{2}{3} \cdot 12) = \frac{3}{2} \cdot 28$

Step 2.1.1.4

Cancel the common factor of $3$ .

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Step 2.1.1.4.1

Factor $3$ out of $12$ .

$\frac{3}{2} (4 t + \frac{2}{3} \cdot (3 (4))) = \frac{3}{2} \cdot 28$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{3}{2} (4 t + \frac{2}{3} \cdot (3 \cdot 4)) = \frac{3}{2} \cdot 28$

Step 2.1.1.4.3

Rewrite the expression.

$\frac{3}{2} (4 t + 2 \cdot 4) = \frac{3}{2} \cdot 28$

Step 2.1.1.5

Multiply $2$ by $4$ .

$\frac{3}{2} (4 t + 8) = \frac{3}{2} \cdot 28$

Step 2.1.1.6

Apply the distributive property.

$\frac{3}{2} (4 t) + \frac{3}{2} \cdot 8 = \frac{3}{2} \cdot 28$

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $4 t$ .

$\frac{3}{2} (2 (2 t)) + \frac{3}{2} \cdot 8 = \frac{3}{2} \cdot 28$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{3}{2} (2 (2 t)) + \frac{3}{2} \cdot 8 = \frac{3}{2} \cdot 28$

Step 2.1.1.7.3

Rewrite the expression.

$3 (2 t) + \frac{3}{2} \cdot 8 = \frac{3}{2} \cdot 28$

Step 2.1.1.8

Multiply $2$ by $3$ .

$6 t + \frac{3}{2} \cdot 8 = \frac{3}{2} \cdot 28$

Step 2.1.1.9

Cancel the common factor of $2$ .

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Step 2.1.1.9.1

Factor $2$ out of $8$ .

$6 t + \frac{3}{2} \cdot (2 (4)) = \frac{3}{2} \cdot 28$

Step 2.1.1.9.2

Cancel the common factor.

$6 t + \frac{3}{2} \cdot (2 \cdot 4) = \frac{3}{2} \cdot 28$

Step 2.1.1.9.3

Rewrite the expression.

$6 t + 3 \cdot 4 = \frac{3}{2} \cdot 28$

Step 2.1.1.10

Multiply $3$ by $4$ .

$6 t + 12 = \frac{3}{2} \cdot 28$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot 28$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $28$ .

$6 t + 12 = \frac{3}{2} \cdot (2 (14))$

Step 2.2.1.1.2

Cancel the common factor.

$6 t + 12 = \frac{3}{2} \cdot (2 \cdot 14)$

Step 2.2.1.1.3

Rewrite the expression.

$6 t + 12 = 3 \cdot 14$

Step 2.2.1.2

Multiply $3$ by $14$ .

$6 t + 12 = 42$

Step 3

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

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Step 3.1

Subtract $12$ from both sides of the equation.

$6 t = 42 - 12$

Step 3.2

Subtract $12$ from $42$ .

$6 t = 30$

Step 4

Divide each term in $6 t = 30$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 t = 30$ by $6$ .

$\frac{6 t}{6} = \frac{30}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 t}{6} = \frac{30}{6}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{30}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $30$ by $6$ .

$t = 5$