Algebra Examples

$- 6 x + \frac{8}{6} - \frac{3}{2} x - \frac{1}{2} + \frac{5}{2} x$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $8$ and $6$ .

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Step 1.1.1

Factor $2$ out of $8$ .

$- 6 x + \frac{2 (4)}{6} - \frac{3}{2} x - \frac{1}{2} + \frac{5}{2} x$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $6$ .

$- 6 x + \frac{2 \cdot 4}{2 \cdot 3} - \frac{3}{2} x - \frac{1}{2} + \frac{5}{2} x$

Step 1.1.2.2

Cancel the common factor.

$- 6 x + \frac{2 \cdot 4}{2 \cdot 3} - \frac{3}{2} x - \frac{1}{2} + \frac{5}{2} x$

Step 1.1.2.3

Rewrite the expression.

$- 6 x + \frac{4}{3} - \frac{3}{2} x - \frac{1}{2} + \frac{5}{2} x$

Step 1.2

Combine $x$ and $\frac{3}{2}$ .

$- 6 x + \frac{4}{3} - \frac{x \cdot 3}{2} - \frac{1}{2} + \frac{5}{2} x$

Step 1.3

Move $3$ to the left of $x$ .

$- 6 x + \frac{4}{3} - \frac{3 \cdot x}{2} - \frac{1}{2} + \frac{5}{2} x$

Step 1.4

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

$- 6 x + \frac{4}{3} - \frac{3 x}{2} - \frac{1}{2} + \frac{5 x}{2}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- 6 x + \frac{4}{3} + \frac{- 3 x - 1 + 5 x}{2}$

Step 2.2

Add $- 3 x$ and $5 x$ .

$- 6 x + \frac{4}{3} + \frac{2 x - 1}{2}$

Step 3

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

$- 6 x \cdot \frac{2}{2} + \frac{2 x - 1}{2} + \frac{4}{3}$

Step 4

Simplify terms.

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Step 4.1

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

$\frac{- 6 x \cdot 2}{2} + \frac{2 x - 1}{2} + \frac{4}{3}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{- 6 x \cdot 2 + 2 x - 1}{2} + \frac{4}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $- 6$ .

$\frac{- 12 x + 2 x - 1}{2} + \frac{4}{3}$

Step 5.2

Add $- 12 x$ and $2 x$ .

$\frac{- 10 x - 1}{2} + \frac{4}{3}$

Step 6

To write $\frac{- 10 x - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- 10 x - 1}{2} \cdot \frac{3}{3} + \frac{4}{3}$

Step 7

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- 10 x - 1}{2} \cdot \frac{3}{3} + \frac{4}{3} \cdot \frac{2}{2}$

Step 8

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{- 10 x - 1}{2}$ by $\frac{3}{3}$ .

$\frac{(- 10 x - 1) \cdot 3}{2 \cdot 3} + \frac{4}{3} \cdot \frac{2}{2}$

Step 8.2

Multiply $2$ by $3$ .

$\frac{(- 10 x - 1) \cdot 3}{6} + \frac{4}{3} \cdot \frac{2}{2}$

Step 8.3

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$\frac{(- 10 x - 1) \cdot 3}{6} + \frac{4 \cdot 2}{3 \cdot 2}$

Step 8.4

Multiply $3$ by $2$ .

$\frac{(- 10 x - 1) \cdot 3}{6} + \frac{4 \cdot 2}{6}$

Step 9

Combine the numerators over the common denominator.

$\frac{(- 10 x - 1) \cdot 3 + 4 \cdot 2}{6}$

Step 10

Simplify the numerator.

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Step 10.1

Apply the distributive property.

$\frac{- 10 x \cdot 3 - 1 \cdot 3 + 4 \cdot 2}{6}$

Step 10.2

Multiply $3$ by $- 10$ .

$\frac{- 30 x - 1 \cdot 3 + 4 \cdot 2}{6}$

Step 10.3

Multiply $- 1$ by $3$ .

$\frac{- 30 x - 3 + 4 \cdot 2}{6}$

Step 10.4

Multiply $4$ by $2$ .

$\frac{- 30 x - 3 + 8}{6}$

Step 10.5

Add $- 3$ and $8$ .

$\frac{- 30 x + 5}{6}$

Step 10.6

Factor $5$ out of $- 30 x + 5$ .

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Step 10.6.1

Factor $5$ out of $- 30 x$ .

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

Step 10.6.2

Factor $5$ out of $5$ .

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

Step 10.6.3

Factor $5$ out of $5 (- 6 x) + 5 (1)$ .

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

Step 11

Simplify with factoring out.

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Step 11.1

Factor $- 1$ out of $- 6 x$ .

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

Step 11.2

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

$\frac{5 (- (6 x) - 1 (- 1))}{6}$

Step 11.3

Factor $- 1$ out of $- (6 x) - 1 (- 1)$ .

$\frac{5 (- (6 x - 1))}{6}$

Step 11.4

Simplify the expression.

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Step 11.4.1

Rewrite $- (6 x - 1)$ as $- 1 (6 x - 1)$ .

$\frac{5 (- 1 (6 x - 1))}{6}$

Step 11.4.2

Move the negative in front of the fraction.

$- \frac{5 (6 x - 1)}{6}$