Algebra Examples

$\frac{3}{5} b - 2 + 7 b - 12 - \frac{2}{5} b + 14$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{3}{5}$ and $b$ .

$\frac{3 b}{5} - 2 + 7 b - 12 - \frac{2}{5} b + 14$

Step 1.2

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

$\frac{3 b}{5} - 2 + 7 b - 12 - \frac{b \cdot 2}{5} + 14$

Step 1.3

Move $2$ to the left of $b$ .

$\frac{3 b}{5} - 2 + 7 b - 12 - \frac{2 b}{5} + 14$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- 2 + 7 b - 12 + 14 + \frac{3 b - 2 b}{5}$

Step 2.2

Subtract $2 b$ from $3 b$ .

$- 2 + 7 b - 12 + 14 + \frac{b}{5}$

Step 2.3

Subtract $12$ from $- 2$ .

$7 b - 14 + 14 + \frac{b}{5}$

Step 2.4

Combine the opposite terms in $7 b - 14 + 14 + \frac{b}{5}$ .

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Step 2.4.1

Add $- 14$ and $14$ .

$7 b + 0 + \frac{b}{5}$

Step 2.4.2

Add $7 b$ and $0$ .

$7 b + \frac{b}{5}$

Step 3

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

$7 b \cdot \frac{5}{5} + \frac{b}{5}$

Step 4

Simplify terms.

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Step 4.1

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

$\frac{7 b \cdot 5}{5} + \frac{b}{5}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{7 b \cdot 5 + b}{5}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $b$ out of $7 b \cdot 5 + b$ .

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Step 5.1.1

Factor $b$ out of $7 b \cdot 5$ .

$\frac{b (7 \cdot 5) + b}{5}$

Step 5.1.2

Raise $b$ to the power of $1$ .

$\frac{b (7 \cdot 5) + b^{1}}{5}$

Step 5.1.3

Factor $b$ out of $b^{1}$ .

$\frac{b (7 \cdot 5) + b \cdot 1}{5}$

Step 5.1.4

Factor $b$ out of $b (7 \cdot 5) + b \cdot 1$ .

$\frac{b (7 \cdot 5 + 1)}{5}$

Step 5.2

Multiply $7$ by $5$ .

$\frac{b (35 + 1)}{5}$

Step 5.3

Add $35$ and $1$ .

$\frac{b \cdot 36}{5}$

Step 6

Move $36$ to the left of $b$ .

$\frac{36 b}{5}$