Linear Algebra Examples

$6 a - 2 (2 a - 1) = 12$

Step 1

Simplify $6 a - 2 (2 a - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 a - 2 (2 a) - 2 \cdot - 1 = 12$

Step 1.1.2

Multiply $2$ by $- 2$ .

$6 a - 4 a - 2 \cdot - 1 = 12$

Step 1.1.3

Multiply $- 2$ by $- 1$ .

$6 a - 4 a + 2 = 12$

Step 1.2

Subtract $4 a$ from $6 a$ .

$2 a + 2 = 12$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

$2 a = 12 - 2$

Step 2.2

Subtract $2$ from $12$ .

$2 a = 10$

Step 3

Divide each term in $2 a = 10$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 a = 10$ by $2$ .

$\frac{2 a}{2} = \frac{10}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{10}{2}$

Step 3.2.1.2

Divide $a$ by $1$ .

$a = \frac{10}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $10$ by $2$ .

$a = 5$

Step 4

The domain is the set of all valid $a$ values.

${a | a = 5}$

Step 5