Basic Math Examples

$\frac{2 \cdot a}{3} = a - 2$

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

$2 \cdot a = (a - 2) \cdot 3$

$2 a = (a - 2) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(a - 2) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$2 a = a \cdot 3 - 2 \cdot 3$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $3$ to the left of $a$ .

$2 a = 3 \cdot a - 2 \cdot 3$

Step 2.2.1.2.2

Multiply $- 2$ by $3$ .

$2 a = 3 a - 6$

Step 3

Solve for $a$ .

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Step 3.1

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

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Step 3.1.1

Subtract $3 a$ from both sides of the equation.

$2 a - 3 a = - 6$

Step 3.1.2

Subtract $3 a$ from $2 a$ .

$- a = - 6$

Step 3.2

Divide each term in $- a = - 6$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- a = - 6$ by $- 1$ .

$\frac{- a}{- 1} = \frac{- 6}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{- 6}{- 1}$

Step 3.2.2.2

Divide $a$ by $1$ .

$a = \frac{- 6}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 6$ by $- 1$ .

$a = 6$