Finite Math Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Cancel the common factor of $6$ and $4$ .

Tap for more steps...

Step 1.1.1

Factor $2$ out of $6$ .

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

Step 1.1.2

Cancel the common factors.

Tap for more steps...

Step 1.1.2.1

Factor $2$ out of $4$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Find the common denominator.

Tap for more steps...

Step 1.5.1

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

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

Step 1.5.2

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

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

Step 1.5.3

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

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

Step 1.5.4

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

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

Step 1.5.5

Write $3$ as a fraction with denominator $1$ .

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

Step 1.5.6

Multiply $\frac{3}{1}$ by $\frac{6}{6}$ .

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

Step 1.5.7

Multiply $\frac{3}{1}$ by $\frac{6}{6}$ .

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

Step 1.5.8

Reorder the factors of $3 \cdot 2$ .

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

Step 1.5.9

Multiply $2$ by $3$ .

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

Step 1.5.10

Multiply $2$ by $3$ .

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

Step 1.6

Combine the numerators over the common denominator.

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

Step 1.7

Simplify each term.

Tap for more steps...

Step 1.7.1

Multiply $3$ by $2$ .

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

Step 1.7.2

Subtract $x$ from $6 x$ .

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

Step 1.7.3

Multiply $2$ by $5$ .

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

Step 1.7.4

Multiply $3$ by $3$ .

$\frac{10 x + 9 + 3 \cdot 6}{6} = 4 x - \frac{3}{6}$

Step 1.7.5

Multiply $3$ by $6$ .

$\frac{10 x + 9 + 18}{6} = 4 x - \frac{3}{6}$

Step 1.8

Add $9$ and $18$ .

$\frac{10 x + 27}{6} = 4 x - \frac{3}{6}$

Step 2

Cancel the common factor of $3$ and $6$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $3$ .

$\frac{10 x + 27}{6} = 4 x - \frac{3 (1)}{6}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $3$ out of $6$ .

$\frac{10 x + 27}{6} = 4 x - \frac{3 \cdot 1}{3 \cdot 2}$

Step 2.2.2

Cancel the common factor.

$\frac{10 x + 27}{6} = 4 x - \frac{3 \cdot 1}{3 \cdot 2}$

Step 2.2.3

Rewrite the expression.

$\frac{10 x + 27}{6} = 4 x - \frac{1}{2}$

Step 3

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $4 x$ from both sides of the equation.

$\frac{10 x + 27}{6} - 4 x = - \frac{1}{2}$

Step 3.2

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{10 x + 27}{6} - 4 x \cdot \frac{6}{6} = - \frac{1}{2}$

Step 3.3

Combine $- 4 x$ and $\frac{6}{6}$ .

$\frac{10 x + 27}{6} + \frac{- 4 x \cdot 6}{6} = - \frac{1}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{10 x + 27 - 4 x \cdot 6}{6} = - \frac{1}{2}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $6$ by $- 4$ .

$\frac{10 x + 27 - 24 x}{6} = - \frac{1}{2}$

Step 3.5.2

Subtract $24 x$ from $10 x$ .

$\frac{- 14 x + 27}{6} = - \frac{1}{2}$

Step 3.6

Factor $- 1$ out of $- 14 x$ .

$\frac{- (14 x) + 27}{6} = - \frac{1}{2}$

Step 3.7

Rewrite $27$ as $- 1 (- 27)$ .

$\frac{- (14 x) - 1 (- 27)}{6} = - \frac{1}{2}$

Step 3.8

Factor $- 1$ out of $- (14 x) - 1 (- 27)$ .

$\frac{- (14 x - 27)}{6} = - \frac{1}{2}$

Step 3.9

Rewrite $- (14 x - 27)$ as $- 1 (14 x - 27)$ .

$\frac{- 1 (14 x - 27)}{6} = - \frac{1}{2}$

Step 3.10

Move the negative in front of the fraction.

$- \frac{14 x - 27}{6} = - \frac{1}{2}$

Step 4

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{14 x - 27}{6}) = - 6 (- \frac{1}{2})$

Step 5

Simplify both sides of the equation.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Simplify $- 6 (- \frac{14 x - 27}{6})$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 5.1.1.1.1

Move the leading negative in $- \frac{14 x - 27}{6}$ into the numerator.

$- 6 \frac{- (14 x - 27)}{6} = - 6 (- \frac{1}{2})$

Step 5.1.1.1.2

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- (14 x - 27)}{6} = - 6 (- \frac{1}{2})$

Step 5.1.1.1.3

Cancel the common factor.

$6 \cdot - 1 \frac{- (14 x - 27)}{6} = - 6 (- \frac{1}{2})$

Step 5.1.1.1.4

Rewrite the expression.

$- - (14 x - 27) = - 6 (- \frac{1}{2})$

Step 5.1.1.2

Multiply.

Tap for more steps...

Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (14 x - 27) = - 6 (- \frac{1}{2})$

Step 5.1.1.2.2

Multiply $14 x - 27$ by $1$ .

$14 x - 27 = - 6 (- \frac{1}{2})$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $- 6 (- \frac{1}{2})$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$14 x - 27 = - 6 (\frac{- 1}{2})$

Step 5.2.1.1.2

Factor $2$ out of $- 6$ .

$14 x - 27 = 2 (- 3) \frac{- 1}{2}$

Step 5.2.1.1.3

Cancel the common factor.

$14 x - 27 = 2 \cdot - 3 \frac{- 1}{2}$

Step 5.2.1.1.4

Rewrite the expression.

$14 x - 27 = - 3 \cdot - 1$

Step 5.2.1.2

Multiply $- 3$ by $- 1$ .

$14 x - 27 = 3$

Step 6

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 6.1

Add $27$ to both sides of the equation.

$14 x = 3 + 27$

Step 6.2

Add $3$ and $27$ .

$14 x = 30$

Step 7

Divide each term in $14 x = 30$ by $14$ and simplify.

Tap for more steps...

Step 7.1

Divide each term in $14 x = 30$ by $14$ .

$\frac{14 x}{14} = \frac{30}{14}$

Step 7.2

Simplify the left side.

Tap for more steps...

Step 7.2.1

Cancel the common factor of $14$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor.

$\frac{14 x}{14} = \frac{30}{14}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{14}$

Step 7.3

Simplify the right side.

Tap for more steps...

Step 7.3.1

Cancel the common factor of $30$ and $14$ .

Tap for more steps...

Step 7.3.1.1

Factor $2$ out of $30$ .

$x = \frac{2 (15)}{14}$

Step 7.3.1.2

Cancel the common factors.

Tap for more steps...

Step 7.3.1.2.1

Factor $2$ out of $14$ .

$x = \frac{2 \cdot 15}{2 \cdot 7}$

Step 7.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 15}{2 \cdot 7}$

Step 7.3.1.2.3

Rewrite the expression.

$x = \frac{15}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{7}$

Decimal Form:

$x = 2.\overline{142857}$

Mixed Number Form:

$x = 2 \frac{1}{7}$