Linear Algebra Examples

$3 x - x - 2 x - 6 x + 6 = 4 x - 2$

Step 1

Simplify $3 x - x - 2 x - 6 x + 6$ .

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Step 1.1

Subtract $x$ from $3 x$ .

$2 x - 2 x - 6 x + 6 = 4 x - 2$

Step 1.2

Subtract $2 x$ from $2 x$ .

$0 - 6 x + 6 = 4 x - 2$

Step 1.3

Subtract $6 x$ from $0$ .

$- 6 x + 6 = 4 x - 2$

Step 2

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

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Step 2.1

Subtract $4 x$ from both sides of the equation.

$- 6 x + 6 - 4 x = - 2$

Step 2.2

Subtract $4 x$ from $- 6 x$ .

$- 10 x + 6 = - 2$

Step 3

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

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Step 3.1

Subtract $6$ from both sides of the equation.

$- 10 x = - 2 - 6$

Step 3.2

Subtract $6$ from $- 2$ .

$- 10 x = - 8$

Step 4

Divide each term in $- 10 x = - 8$ by $- 10$ and simplify.

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Step 4.1

Divide each term in $- 10 x = - 8$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 8}{- 10}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 10$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 8}{- 10}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 10}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 8$ and $- 10$ .

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Step 4.3.1.1

Factor $- 2$ out of $- 8$ .

$x = \frac{- 2 (4)}{- 10}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $- 2$ out of $- 10$ .

$x = \frac{- 2 \cdot 4}{- 2 \cdot 5}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 4}{- 2 \cdot 5}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{4}{5}$

Step 5

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

${x | x = \frac{4}{5}}$

Step 6