Linear Algebra Examples

$6 (w - 2) + 2 = 2 (v + 1)$

Step 1

Simplify $6 (w - 2) + 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 w + 6 \cdot - 2 + 2 = 2 (v + 1)$

Step 1.1.2

Multiply $6$ by $- 2$ .

$6 w - 12 + 2 = 2 (v + 1)$

Step 1.2

Add $- 12$ and $2$ .

$6 w - 10 = 2 (v + 1)$

Step 2

Simplify $2 (v + 1)$ .

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Step 2.1

Apply the distributive property.

$6 w - 10 = 2 v + 2 \cdot 1$

Step 2.2

Multiply $2$ by $1$ .

$6 w - 10 = 2 v + 2$

Step 3

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

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Step 3.1

Add $10$ to both sides of the equation.

$6 w = 2 v + 2 + 10$

Step 3.2

Add $2$ and $10$ .

$6 w = 2 v + 12$

Step 4

Divide each term in $6 w = 2 v + 12$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 w = 2 v + 12$ by $6$ .

$\frac{6 w}{6} = \frac{2 v}{6} + \frac{12}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 w}{6} = \frac{2 v}{6} + \frac{12}{6}$

Step 4.2.1.2

Divide $w$ by $1$ .

$w = \frac{2 v}{6} + \frac{12}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $2$ and $6$ .

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Step 4.3.1.1.1

Factor $2$ out of $2 v$ .

$w = \frac{2 (v)}{6} + \frac{12}{6}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Factor $2$ out of $6$ .

$w = \frac{2 v}{2 \cdot 3} + \frac{12}{6}$

Step 4.3.1.1.2.2

Cancel the common factor.

$w = \frac{2 v}{2 \cdot 3} + \frac{12}{6}$

Step 4.3.1.1.2.3

Rewrite the expression.

$w = \frac{v}{3} + \frac{12}{6}$

Step 4.3.1.2

Divide $12$ by $6$ .

$w = \frac{v}{3} + 2$

Step 5

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 6