Linear Algebra Examples

$0.2 (x + 2) - 0.5 (x + 2) = 0.3 x - 0.6$

Step 1

Simplify $0.2 (x + 2) - 0.5 (x + 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$0.2 x + 0.2 \cdot 2 - 0.5 (x + 2) = 0.3 x - 0.6$

Step 1.1.2

Multiply $0.2$ by $2$ .

$0.2 x + 0.4 - 0.5 (x + 2) = 0.3 x - 0.6$

Step 1.1.3

Apply the distributive property.

$0.2 x + 0.4 - 0.5 x - 0.5 \cdot 2 = 0.3 x - 0.6$

Step 1.1.4

Multiply $- 0.5$ by $2$ .

$0.2 x + 0.4 - 0.5 x - 1 = 0.3 x - 0.6$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $0.5 x$ from $0.2 x$ .

$- 0.3 x + 0.4 - 1 = 0.3 x - 0.6$

Step 1.2.2

Subtract $1$ from $0.4$ .

$- 0.3 x - 0.6 = 0.3 x - 0.6$

Step 2

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

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Step 2.1

Subtract $0.3 x$ from both sides of the equation.

$- 0.3 x - 0.6 - 0.3 x = - 0.6$

Step 2.2

Subtract $0.3 x$ from $- 0.3 x$ .

$- 0.6 x - 0.6 = - 0.6$

Step 3

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

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Step 3.1

Add $0.6$ to both sides of the equation.

$- 0.6 x = - 0.6 + 0.6$

Step 3.2

Add $- 0.6$ and $0.6$ .

$- 0.6 x = 0$

Step 4

Divide each term in $- 0.6 x = 0$ by $- 0.6$ and simplify.

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Step 4.1

Divide each term in $- 0.6 x = 0$ by $- 0.6$ .

$\frac{- 0.6 x}{- 0.6} = \frac{0}{- 0.6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 0.6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 0.6 x}{- 0.6} = \frac{0}{- 0.6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{- 0.6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $- 0.6$ .

$x = 0$

Step 5

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

${x | x = 0}$

Step 6