Algebra Examples

$\frac{5}{7} x + \frac{2}{7} y - 2 - \frac{1}{7} x + 7$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{5}{7}$ and $x$ .

$\frac{5 x}{7} + \frac{2}{7} y - 2 - \frac{1}{7} x + 7$

Step 1.2

Combine $\frac{2}{7}$ and $y$ .

$\frac{5 x}{7} + \frac{2 y}{7} - 2 - \frac{1}{7} x + 7$

Step 1.3

Combine $x$ and $\frac{1}{7}$ .

$\frac{5 x}{7} + \frac{2 y}{7} - 2 - \frac{x}{7} + 7$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- 2 + 7 + \frac{5 x + 2 y - x}{7}$

Step 2.2

Subtract $x$ from $5 x$ .

$- 2 + 7 + \frac{4 x + 2 y}{7}$

Step 2.3

Factor $2$ out of $4 x + 2 y$ .

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Step 2.3.1

Factor $2$ out of $4 x$ .

$- 2 + 7 + \frac{2 (2 x) + 2 y}{7}$

Step 2.3.2

Factor $2$ out of $2 y$ .

$- 2 + 7 + \frac{2 (2 x) + 2 (y)}{7}$

Step 2.3.3

Factor $2$ out of $2 (2 x) + 2 (y)$ .

$- 2 + 7 + \frac{2 (2 x + y)}{7}$

Step 2.4

Add $- 2$ and $7$ .

$5 + \frac{2 (2 x + y)}{7}$

Step 3

To write $5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$5 \cdot \frac{7}{7} + \frac{2 (2 x + y)}{7}$

Step 4

Simplify terms.

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Step 4.1

Combine $5$ and $\frac{7}{7}$ .

$\frac{5 \cdot 7}{7} + \frac{2 (2 x + y)}{7}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{5 \cdot 7 + 2 (2 x + y)}{7}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $7$ .

$\frac{35 + 2 (2 x + y)}{7}$

Step 5.2

Apply the distributive property.

$\frac{35 + 2 (2 x) + 2 y}{7}$

Step 5.3

Multiply $2$ by $2$ .

$\frac{35 + 4 x + 2 y}{7}$