Basic Math Examples

$3 (3 a - 2) = \frac{3}{4} \cdot (4 - 24 a)$

Step 1

Simplify $3 (3 a - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (3 a - 2) = \frac{3}{4} \cdot (4 - 24 a)$

Step 1.2

Simplify by adding zeros.

$3 (3 a - 2) = \frac{3}{4} \cdot (4 - 24 a)$

Step 1.3

Apply the distributive property.

$3 (3 a) + 3 \cdot - 2 = \frac{3}{4} \cdot (4 - 24 a)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $3$ .

$9 a + 3 \cdot - 2 = \frac{3}{4} \cdot (4 - 24 a)$

Step 1.4.2

Multiply $3$ by $- 2$ .

$9 a - 6 = \frac{3}{4} \cdot (4 - 24 a)$

Step 2

Simplify $\frac{3}{4} \cdot (4 - 24 a)$ .

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Step 2.1

Apply the distributive property.

$9 a - 6 = \frac{3}{4} \cdot 4 + \frac{3}{4} (- 24 a)$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Cancel the common factor.

$9 a - 6 = \frac{3}{4} \cdot 4 + \frac{3}{4} (- 24 a)$

Step 2.2.2

Rewrite the expression.

$9 a - 6 = 3 + \frac{3}{4} (- 24 a)$

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Factor $4$ out of $- 24 a$ .

$9 a - 6 = 3 + \frac{3}{4} (4 (- 6 a))$

Step 2.3.2

Cancel the common factor.

$9 a - 6 = 3 + \frac{3}{4} (4 (- 6 a))$

Step 2.3.3

Rewrite the expression.

$9 a - 6 = 3 + 3 (- 6 a)$

Step 2.4

Multiply $- 6$ by $3$ .

$9 a - 6 = 3 - 18 a$

Step 3

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

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Step 3.1

Add $18 a$ to both sides of the equation.

$9 a - 6 + 18 a = 3$

Step 3.2

Add $9 a$ and $18 a$ .

$27 a - 6 = 3$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$27 a = 3 + 6$

Step 4.2

Add $3$ and $6$ .

$27 a = 9$

Step 5

Divide each term in $27 a = 9$ by $27$ and simplify.

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Step 5.1

Divide each term in $27 a = 9$ by $27$ .

$\frac{27 a}{27} = \frac{9}{27}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $27$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{27 a}{27} = \frac{9}{27}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{9}{27}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $9$ and $27$ .

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Step 5.3.1.1

Factor $9$ out of $9$ .

$a = \frac{9 (1)}{27}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $9$ out of $27$ .

$a = \frac{9 \cdot 1}{9 \cdot 3}$

Step 5.3.1.2.2

Cancel the common factor.

$a = \frac{9 \cdot 1}{9 \cdot 3}$

Step 5.3.1.2.3

Rewrite the expression.

$a = \frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{3}$

Decimal Form:

$a = 0.\overline{3}$