Basic Math Examples

$a (3 b - 1) = 2 b + 2$

Step 1

Simplify $a (3 b - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + a (3 b - 1) = 2 b + 2$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$a (3 b) + a \cdot - 1 = 2 b + 2$

Step 1.2.2

Reorder.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$3 a b + a \cdot - 1 = 2 b + 2$

Step 1.2.2.2

Move $- 1$ to the left of $a$ .

$3 a b - 1 \cdot a = 2 b + 2$

Step 1.3

Rewrite $- 1 a$ as $- a$ .

$3 a b - a = 2 b + 2$

Step 2

Subtract $2 b$ from both sides of the equation.

$3 a b - a - 2 b = 2$

Step 3

Add $a$ to both sides of the equation.

$3 a b - 2 b = 2 + a$

Step 4

Factor $b$ out of $3 a b - 2 b$ .

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Step 4.1

Factor $b$ out of $3 a b$ .

$b (3 a) - 2 b = 2 + a$

Step 4.2

Factor $b$ out of $- 2 b$ .

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

Step 4.3

Factor $b$ out of $b (3 a) + b \cdot - 2$ .

$b (3 a - 2) = 2 + a$

Step 5

Divide each term in $b (3 a - 2) = 2 + a$ by $3 a - 2$ and simplify.

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Step 5.1

Divide each term in $b (3 a - 2) = 2 + a$ by $3 a - 2$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3 a - 2$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{2}{3 a - 2} + \frac{a}{3 a - 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$b = \frac{2 + a}{3 a - 2}$