Algebra Examples

$- 5 (7 + x) + 2 \frac{5}{6} x$

Step 1

Convert $2 \frac{5}{6}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$- 5 (7 + x) + (2 + \frac{5}{6}) x$

Step 1.2

Add $2$ and $\frac{5}{6}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- 5 (7 + x) + (2 \cdot \frac{6}{6} + \frac{5}{6}) x$

Step 1.2.2

Combine $2$ and $\frac{6}{6}$ .

$- 5 (7 + x) + (\frac{2 \cdot 6}{6} + \frac{5}{6}) x$

Step 1.2.3

Combine the numerators over the common denominator.

$- 5 (7 + x) + \frac{2 \cdot 6 + 5}{6} x$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $6$ .

$- 5 (7 + x) + \frac{12 + 5}{6} x$

Step 1.2.4.2

Add $12$ and $5$ .

$- 5 (7 + x) + \frac{17}{6} x$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 5 \cdot 7 - 5 x + \frac{17}{6} x$

Step 2.2

Multiply $- 5$ by $7$ .

$- 35 - 5 x + \frac{17}{6} x$

Step 2.3

Combine $\frac{17}{6}$ and $x$ .

$- 35 - 5 x + \frac{17 x}{6}$

Step 3

To write $- 5 x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- 35 - 5 x \cdot \frac{6}{6} + \frac{17 x}{6}$

Step 4

Simplify terms.

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Step 4.1

Combine $- 5 x$ and $\frac{6}{6}$ .

$- 35 + \frac{- 5 x \cdot 6}{6} + \frac{17 x}{6}$

Step 4.2

Combine the numerators over the common denominator.

$- 35 + \frac{- 5 x \cdot 6 + 17 x}{6}$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $x$ out of $- 5 x \cdot 6 + 17 x$ .

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Step 5.1.1.1

Factor $x$ out of $- 5 x \cdot 6$ .

$- 35 + \frac{x (- 5 \cdot 6) + 17 x}{6}$

Step 5.1.1.2

Factor $x$ out of $17 x$ .

$- 35 + \frac{x (- 5 \cdot 6) + x \cdot 17}{6}$

Step 5.1.1.3

Factor $x$ out of $x (- 5 \cdot 6) + x \cdot 17$ .

$- 35 + \frac{x (- 5 \cdot 6 + 17)}{6}$

Step 5.1.2

Multiply $- 5$ by $6$ .

$- 35 + \frac{x (- 30 + 17)}{6}$

Step 5.1.3

Add $- 30$ and $17$ .

$- 35 + \frac{x \cdot - 13}{6}$

Step 5.2

Move $- 13$ to the left of $x$ .

$- 35 + \frac{- 13 \cdot x}{6}$

Step 5.3

Move the negative in front of the fraction.

$- 35 - \frac{13 x}{6}$