Algebra Examples

$3 a - 5 b = 12 - 4 (b + a)$

Step 1

Apply the distributive property.

$3 a - 5 b = 12 - 4 b - 4 a$

Step 2

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

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Step 2.1

Add $4 a$ to both sides of the equation.

$3 a - 5 b + 4 a = 12 - 4 b$

Step 2.2

Add $3 a$ and $4 a$ .

$7 a - 5 b = 12 - 4 b$

Step 3

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

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Step 3.1

Add $5 b$ to both sides of the equation.

$7 a = 12 - 4 b + 5 b$

Step 3.2

Add $- 4 b$ and $5 b$ .

$7 a = 12 + b$

Step 4

Divide each term in $7 a = 12 + b$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 a = 12 + b$ by $7$ .

$\frac{7 a}{7} = \frac{12}{7} + \frac{b}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 a}{7} = \frac{12}{7} + \frac{b}{7}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{12}{7} + \frac{b}{7}$