Algebra Examples

$\frac{2}{5} y + \frac{1}{5} x - 0.2 y - 6 + (- 2)$

Step 1

Remove parentheses.

$\frac{2}{5} y + \frac{1}{5} x - 0.2 y - 6 - 2$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{2}{5}$ and $y$ .

$\frac{2 y}{5} + \frac{1}{5} x - 0.2 y - 6 - 2$

Step 2.2

Combine $\frac{1}{5}$ and $x$ .

$\frac{2 y}{5} + \frac{x}{5} - 0.2 y - 6 - 2$

Step 3

To write $- 0.2 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{5} + \frac{2 y}{5} - 0.2 y \cdot \frac{5}{5} - 6 - 2$

Step 4

Simplify terms.

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Step 4.1

Combine $- 0.2 y$ and $\frac{5}{5}$ .

$\frac{x}{5} + \frac{2 y}{5} + \frac{- 0.2 y \cdot 5}{5} - 6 - 2$

Step 4.2

Combine the numerators over the common denominator.

$\frac{x}{5} + \frac{2 y - 0.2 y \cdot 5}{5} - 6 - 2$

Step 4.3

Combine the numerators over the common denominator.

$- 6 - 2 + \frac{x + 2 y - 0.2 y \cdot 5}{5}$

Step 5

Simplify each term.

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Step 5.1

Multiply $5$ by $- 0.2$ .

$- 6 - 2 + \frac{x + 2 y - 1 y}{5}$

Step 5.2

Rewrite $- 1 y$ as $- y$ .

$- 6 - 2 + \frac{x + 2 y - y}{5}$

Step 6

Simplify by adding terms.

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Step 6.1

Subtract $y$ from $2 y$ .

$- 6 - 2 + \frac{x + y}{5}$

Step 6.2

Subtract $2$ from $- 6$ .

$- 8 + \frac{x + y}{5}$

Step 7

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 8 \cdot \frac{5}{5} + \frac{x + y}{5}$

Step 8

Combine $- 8$ and $\frac{5}{5}$ .

$\frac{- 8 \cdot 5}{5} + \frac{x + y}{5}$

Step 9

Combine the numerators over the common denominator.

$\frac{- 8 \cdot 5 + x + y}{5}$

Step 10

Multiply $- 8$ by $5$ .

$\frac{- 40 + x + y}{5}$

Step 11

Rewrite $- 40$ as $- 1 (40)$ .

$\frac{- 1 (40) + x + y}{5}$

Step 12

Factor $- 1$ out of $x$ .

$\frac{- 1 (40) - 1 (- x) + y}{5}$

Step 13

Factor $- 1$ out of $- 1 (40) - 1 (- x)$ .

$\frac{- 1 (40 - x) + y}{5}$

Step 14

Factor $- 1$ out of $y$ .

$\frac{- 1 (40 - x) - 1 (- y)}{5}$

Step 15

Factor $- 1$ out of $- 1 (40 - x) - 1 (- y)$ .

$\frac{- 1 (40 - x - y)}{5}$

Step 16

Move the negative in front of the fraction.

$- \frac{40 - x - y}{5}$