Algebra Examples

$0.4 (2 x + \frac{1}{2}) = 3 (0.2 x + (- 2)) - 4$

Step 1

Simplify $0.4 (2 x + \frac{1}{2})$ .

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Step 1.1

Rewrite.

$0 + 0 + 0.4 (2 x + \frac{1}{2}) = 3 (0.2 x - 2) - 4$

Step 1.2

Simplify by adding zeros.

$0.4 (2 x + \frac{1}{2}) = 3 (0.2 x - 2) - 4$

Step 1.3

Apply the distributive property.

$0.4 (2 x) + 0.4 (\frac{1}{2}) = 3 (0.2 x - 2) - 4$

Step 1.4

Multiply $2$ by $0.4$ .

$0.8 x + 0.4 (\frac{1}{2}) = 3 (0.2 x - 2) - 4$

Step 1.5

Cancel the common factor of $0.4$ .

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Step 1.5.1

Factor $0.4$ out of $2$ .

$0.8 x + 0.4 \frac{1}{0.4 (5)} = 3 (0.2 x - 2) - 4$

Step 1.5.2

Cancel the common factor.

$0.8 x + 0.4 \frac{1}{0.4 \cdot 5} = 3 (0.2 x - 2) - 4$

Step 1.5.3

Rewrite the expression.

$0.8 x + \frac{1}{5} = 3 (0.2 x - 2) - 4$

Step 2

Simplify $3 (0.2 x - 2) - 4$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$0.8 x + \frac{1}{5} = 3 (0.2 x) + 3 \cdot - 2 - 4$

Step 2.1.2

Multiply $0.2$ by $3$ .

$0.8 x + \frac{1}{5} = 0.6 x + 3 \cdot - 2 - 4$

Step 2.1.3

Multiply $3$ by $- 2$ .

$0.8 x + \frac{1}{5} = 0.6 x - 6 - 4$

Step 2.2

Subtract $4$ from $- 6$ .

$0.8 x + \frac{1}{5} = 0.6 x - 10$

Step 3

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

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Step 3.1

Subtract $0.6 x$ from both sides of the equation.

$0.8 x + \frac{1}{5} - 0.6 x = - 10$

Step 3.2

Subtract $0.6 x$ from $0.8 x$ .

$0.2 x + \frac{1}{5} = - 10$

Step 4

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

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Step 4.1

Subtract $\frac{1}{5}$ from both sides of the equation.

$0.2 x = - 10 - \frac{1}{5}$

Step 4.2

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$0.2 x = - 10 \cdot \frac{5}{5} - \frac{1}{5}$

Step 4.3

Combine $- 10$ and $\frac{5}{5}$ .

$0.2 x = \frac{- 10 \cdot 5}{5} - \frac{1}{5}$

Step 4.4

Combine the numerators over the common denominator.

$0.2 x = \frac{- 10 \cdot 5 - 1}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 10$ by $5$ .

$0.2 x = \frac{- 50 - 1}{5}$

Step 4.5.2

Subtract $1$ from $- 50$ .

$0.2 x = \frac{- 51}{5}$

Step 4.6

Move the negative in front of the fraction.

$0.2 x = - \frac{51}{5}$

Step 5

Divide each term in $0.2 x = - \frac{51}{5}$ by $0.2$ and simplify.

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Step 5.1

Divide each term in $0.2 x = - \frac{51}{5}$ by $0.2$ .

$\frac{0.2 x}{0.2} = \frac{- \frac{51}{5}}{0.2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $0.2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{0.2 x}{0.2} = \frac{- \frac{51}{5}}{0.2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{51}{5}}{0.2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{51}{5} \cdot \frac{1}{0.2}$

Step 5.3.2

Cancel the common factor of $0.2$ .

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Step 5.3.2.1

Move the leading negative in $- \frac{51}{5}$ into the numerator.

$x = \frac{- 51}{5} \cdot \frac{1}{0.2}$

Step 5.3.2.2

Factor $0.2$ out of $- 51$ .

$x = \frac{0.2 (- 255)}{5} \cdot \frac{1}{0.2}$

Step 5.3.2.3

Cancel the common factor.

$x = \frac{0.2 \cdot - 255}{5} \cdot \frac{1}{0.2}$

Step 5.3.2.4

Rewrite the expression.

$x = \frac{- 255}{5}$

Step 5.3.3

Divide $- 255$ by $5$ .

$x = - 51$