Pre-Algebra Examples

$0.5 x - 0.5 (2 x + 7) = - 0.6 (x + 4)$

Step 1

Simplify $0.5 x - 0.5 (2 x + 7)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$0.5 x - 0.5 (2 x) - 0.5 \cdot 7 = - 0.6 (x + 4)$

Step 1.1.2

Multiply $2$ by $- 0.5$ .

$0.5 x - 1 x - 0.5 \cdot 7 = - 0.6 (x + 4)$

Step 1.1.3

Multiply $- 0.5$ by $7$ .

$0.5 x - 1 x - 3.5 = - 0.6 (x + 4)$

Step 1.1.4

Rewrite $- 1 x$ as $- x$ .

$0.5 x - x - 3.5 = - 0.6 (x + 4)$

Step 1.2

Subtract $x$ from $0.5 x$ .

$- 0.5 x - 3.5 = - 0.6 (x + 4)$

Step 2

Simplify $- 0.6 (x + 4)$ .

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Step 2.1

Apply the distributive property.

$- 0.5 x - 3.5 = - 0.6 x - 0.6 \cdot 4$

Step 2.2

Multiply $- 0.6$ by $4$ .

$- 0.5 x - 3.5 = - 0.6 x - 2.4$

Step 3

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

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Step 3.1

Add $0.6 x$ to both sides of the equation.

$- 0.5 x - 3.5 + 0.6 x = - 2.4$

Step 3.2

Add $- 0.5 x$ and $0.6 x$ .

$0.1 x - 3.5 = - 2.4$

Step 4

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

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Step 4.1

Add $3.5$ to both sides of the equation.

$0.1 x = - 2.4 + 3.5$

Step 4.2

Add $- 2.4$ and $3.5$ .

$0.1 x = 1.1$

Step 5

Divide each term in $0.1 x = 1.1$ by $0.1$ and simplify.

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Step 5.1

Divide each term in $0.1 x = 1.1$ by $0.1$ .

$\frac{0.1 x}{0.1} = \frac{1.1}{0.1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $0.1$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{0.1 x}{0.1} = \frac{1.1}{0.1}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{1.1}{0.1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $1.1$ by $0.1$ .

$x = 11$