Algebra Examples

$4 \frac{1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Simplify $4 \frac{1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3})$ .

Tap for more steps...

Step 1.1.1

Convert $4 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 1.1.1.1

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

$4 + \frac{1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.1.2

Add $4$ and $\frac{1}{2}$ .

Tap for more steps...

Step 1.1.1.2.1

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

$4 \cdot \frac{2}{2} + \frac{1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.1.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{4 \cdot 2}{2} + \frac{1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.1.2.4.1

Multiply $4$ by $2$ .

$\frac{8 + 1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.1.2.4.2

Add $8$ and $1$ .

$\frac{9}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.2

Convert $5 \frac{1}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1.2.1

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

$\frac{9}{2} - (5 + \frac{1}{3}) \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.2.2

Add $5$ and $\frac{1}{3}$ .

Tap for more steps...

Step 1.1.2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{2} - (5 \cdot \frac{3}{3} + \frac{1}{3}) \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.2.2.2

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

$\frac{9}{2} - (\frac{5 \cdot 3}{3} + \frac{1}{3}) \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{5 \cdot 3 + 1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.2.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.2.2.4.1

Multiply $5$ by $3$ .

$\frac{9}{2} - \frac{15 + 1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.2.2.4.2

Add $15$ and $1$ .

$\frac{9}{2} - \frac{16}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$

Step 1.1.3

Convert $14 \frac{2}{3}$ to an improper fraction.

Tap for more steps...

Step 1.1.3.1

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

$\frac{9}{2} - \frac{16}{3} \div (20 x - (14 + \frac{2}{3})) = 1 \frac{5}{6}$

Step 1.1.3.2

Add $14$ and $\frac{2}{3}$ .

Tap for more steps...

Step 1.1.3.2.1

To write $14$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{2} - \frac{16}{3} \div (20 x - (14 \cdot \frac{3}{3} + \frac{2}{3})) = 1 \frac{5}{6}$

Step 1.1.3.2.2

Combine $14$ and $\frac{3}{3}$ .

$\frac{9}{2} - \frac{16}{3} \div (20 x - (\frac{14 \cdot 3}{3} + \frac{2}{3})) = 1 \frac{5}{6}$

Step 1.1.3.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{16}{3} \div (20 x - \frac{14 \cdot 3 + 2}{3}) = 1 \frac{5}{6}$

Step 1.1.3.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.3.2.4.1

Multiply $14$ by $3$ .

$\frac{9}{2} - \frac{16}{3} \div (20 x - \frac{42 + 2}{3}) = 1 \frac{5}{6}$

Step 1.1.3.2.4.2

Add $42$ and $2$ .

$\frac{9}{2} - \frac{16}{3} \div (20 x - \frac{44}{3}) = 1 \frac{5}{6}$

Step 1.1.4

Simplify each term.

Tap for more steps...

Step 1.1.4.1

Rewrite the division as a fraction.

$\frac{9}{2} - \frac{\frac{16}{3}}{20 x - \frac{44}{3}} = 1 \frac{5}{6}$

Step 1.1.4.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{20 x - \frac{44}{3}}) = 1 \frac{5}{6}$

Step 1.1.4.3

Simplify the denominator.

Tap for more steps...

Step 1.1.4.3.1

Factor $4$ out of $20 x - \frac{44}{3}$ .

Tap for more steps...

Step 1.1.4.3.1.1

Factor $4$ out of $20 x$ .

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{4 (5 x) - \frac{44}{3}}) = 1 \frac{5}{6}$

Step 1.1.4.3.1.2

Factor $4$ out of $- \frac{44}{3}$ .

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{4 (5 x) + 4 (- \frac{11}{3})}) = 1 \frac{5}{6}$

Step 1.1.4.3.1.3

Factor $4$ out of $4 (5 x) + 4 (- \frac{11}{3})$ .

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{4 (5 x - \frac{11}{3})}) = 1 \frac{5}{6}$

Step 1.1.4.3.2

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{4 (5 x \cdot \frac{3}{3} - \frac{11}{3})}) = 1 \frac{5}{6}$

Step 1.1.4.3.3

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

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{4 (\frac{5 x \cdot 3}{3} - \frac{11}{3})}) = 1 \frac{5}{6}$

Step 1.1.4.3.4

Combine the numerators over the common denominator.

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{4 \frac{5 x \cdot 3 - 11}{3}}) = 1 \frac{5}{6}$

Step 1.1.4.3.5

Multiply $3$ by $5$ .

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{4 \frac{15 x - 11}{3}}) = 1 \frac{5}{6}$

Step 1.1.4.4

Combine $4$ and $\frac{15 x - 11}{3}$ .

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{1}{\frac{4 (15 x - 11)}{3}}) = 1 \frac{5}{6}$

Step 1.1.4.5

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{2} - (\frac{16}{3} (1 \frac{3}{4 (15 x - 11)})) = 1 \frac{5}{6}$

Step 1.1.4.6

Multiply $\frac{3}{4 (15 x - 11)}$ by $1$ .

$\frac{9}{2} - (\frac{16}{3} \cdot \frac{3}{4 (15 x - 11)}) = 1 \frac{5}{6}$

Step 1.1.4.7

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.1.4.7.1

Factor $4$ out of $16$ .

$\frac{9}{2} - (\frac{4 (4)}{3} \cdot \frac{3}{4 (15 x - 11)}) = 1 \frac{5}{6}$

Step 1.1.4.7.2

Cancel the common factor.

$\frac{9}{2} - (\frac{4 \cdot 4}{3} \cdot \frac{3}{4 (15 x - 11)}) = 1 \frac{5}{6}$

Step 1.1.4.7.3

Rewrite the expression.

$\frac{9}{2} - (\frac{4}{3} \cdot \frac{3}{15 x - 11}) = 1 \frac{5}{6}$

Step 1.1.4.8

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.1.4.8.1

Cancel the common factor.

$\frac{9}{2} - (\frac{4}{3} \cdot \frac{3}{15 x - 11}) = 1 \frac{5}{6}$

Step 1.1.4.8.2

Rewrite the expression.

$\frac{9}{2} - (4 \frac{1}{15 x - 11}) = 1 \frac{5}{6}$

Step 1.1.4.9

Combine $4$ and $\frac{1}{15 x - 11}$ .

$\frac{9}{2} - \frac{4}{15 x - 11} = 1 \frac{5}{6}$

Step 1.1.5

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{15 x - 11}{15 x - 11}$ .

$\frac{9}{2} \cdot \frac{15 x - 11}{15 x - 11} - \frac{4}{15 x - 11} = 1 \frac{5}{6}$

Step 1.1.6

To write $- \frac{4}{15 x - 11}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{2} \cdot \frac{15 x - 11}{15 x - 11} - \frac{4}{15 x - 11} \cdot \frac{2}{2} = 1 \frac{5}{6}$

Step 1.1.7

Write each expression with a common denominator of $2 (15 x - 11)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.1.7.1

Multiply $\frac{9}{2}$ by $\frac{15 x - 11}{15 x - 11}$ .

$\frac{9 (15 x - 11)}{2 (15 x - 11)} - \frac{4}{15 x - 11} \cdot \frac{2}{2} = 1 \frac{5}{6}$

Step 1.1.7.2

Multiply $\frac{4}{15 x - 11}$ by $\frac{2}{2}$ .

$\frac{9 (15 x - 11)}{2 (15 x - 11)} - \frac{4 \cdot 2}{(15 x - 11) \cdot 2} = 1 \frac{5}{6}$

Step 1.1.7.3

Reorder the factors of $(15 x - 11) \cdot 2$ .

$\frac{9 (15 x - 11)}{2 (15 x - 11)} - \frac{4 \cdot 2}{2 (15 x - 11)} = 1 \frac{5}{6}$

Step 1.1.8

Combine the numerators over the common denominator.

$\frac{9 (15 x - 11) - 4 \cdot 2}{2 (15 x - 11)} = 1 \frac{5}{6}$

Step 1.1.9

Simplify the numerator.

Tap for more steps...

Step 1.1.9.1

Apply the distributive property.

$\frac{9 (15 x) + 9 \cdot - 11 - 4 \cdot 2}{2 (15 x - 11)} = 1 \frac{5}{6}$

Step 1.1.9.2

Multiply $15$ by $9$ .

$\frac{135 x + 9 \cdot - 11 - 4 \cdot 2}{2 (15 x - 11)} = 1 \frac{5}{6}$

Step 1.1.9.3

Multiply $9$ by $- 11$ .

$\frac{135 x - 99 - 4 \cdot 2}{2 (15 x - 11)} = 1 \frac{5}{6}$

Step 1.1.9.4

Multiply $- 4$ by $2$ .

$\frac{135 x - 99 - 8}{2 (15 x - 11)} = 1 \frac{5}{6}$

Step 1.1.9.5

Subtract $8$ from $- 99$ .

$\frac{135 x - 107}{2 (15 x - 11)} = 1 \frac{5}{6}$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Convert $1 \frac{5}{6}$ to an improper fraction.

Tap for more steps...

Step 2.1.1

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

$\frac{135 x - 107}{2 (15 x - 11)} = 1 + \frac{5}{6}$

Step 2.1.2

Add $1$ and $\frac{5}{6}$ .

Tap for more steps...

Step 2.1.2.1

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

$\frac{135 x - 107}{2 (15 x - 11)} = \frac{6}{6} + \frac{5}{6}$

Step 2.1.2.2

Combine the numerators over the common denominator.

$\frac{135 x - 107}{2 (15 x - 11)} = \frac{6 + 5}{6}$

Step 2.1.2.3

Add $6$ and $5$ .

$\frac{135 x - 107}{2 (15 x - 11)} = \frac{11}{6}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$(135 x - 107) \cdot 6 = 2 (15 x - 11) \cdot 11$

Step 4

Solve the equation for $x$ .

Tap for more steps...

Step 4.1

Simplify $(135 x - 107) \cdot 6$ .

Tap for more steps...

Step 4.1.1

Rewrite.

$0 + 0 + (135 x - 107) \cdot 6 = 2 (15 x - 11) \cdot 11$

Step 4.1.2

Simplify by adding zeros.

$(135 x - 107) \cdot 6 = 2 (15 x - 11) \cdot 11$

Step 4.1.3

Apply the distributive property.

$135 x \cdot 6 - 107 \cdot 6 = 2 (15 x - 11) \cdot 11$

Step 4.1.4

Multiply.

Tap for more steps...

Step 4.1.4.1

Multiply $6$ by $135$ .

$810 x - 107 \cdot 6 = 2 (15 x - 11) \cdot 11$

Step 4.1.4.2

Multiply $- 107$ by $6$ .

$810 x - 642 = 2 (15 x - 11) \cdot 11$

Step 4.2

Simplify $2 (15 x - 11) \cdot 11$ .

Tap for more steps...

Step 4.2.1

Apply the distributive property.

$810 x - 642 = (2 (15 x) + 2 \cdot - 11) \cdot 11$

Step 4.2.2

Multiply.

Tap for more steps...

Step 4.2.2.1

Multiply $15$ by $2$ .

$810 x - 642 = (30 x + 2 \cdot - 11) \cdot 11$

Step 4.2.2.2

Multiply $2$ by $- 11$ .

$810 x - 642 = (30 x - 22) \cdot 11$

Step 4.2.3

Apply the distributive property.

$810 x - 642 = 30 x \cdot 11 - 22 \cdot 11$

Step 4.2.4

Multiply.

Tap for more steps...

Step 4.2.4.1

Multiply $11$ by $30$ .

$810 x - 642 = 330 x - 22 \cdot 11$

Step 4.2.4.2

Multiply $- 22$ by $11$ .

$810 x - 642 = 330 x - 242$

Step 4.3

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

Tap for more steps...

Step 4.3.1

Subtract $330 x$ from both sides of the equation.

$810 x - 642 - 330 x = - 242$

Step 4.3.2

Subtract $330 x$ from $810 x$ .

$480 x - 642 = - 242$

Step 4.4

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

Tap for more steps...

Step 4.4.1

Add $642$ to both sides of the equation.

$480 x = - 242 + 642$

Step 4.4.2

Add $- 242$ and $642$ .

$480 x = 400$

Step 4.5

Divide each term in $480 x = 400$ by $480$ and simplify.

Tap for more steps...

Step 4.5.1

Divide each term in $480 x = 400$ by $480$ .

$\frac{480 x}{480} = \frac{400}{480}$

Step 4.5.2

Simplify the left side.

Tap for more steps...

Step 4.5.2.1

Cancel the common factor of $480$ .

Tap for more steps...

Step 4.5.2.1.1

Cancel the common factor.

$\frac{480 x}{480} = \frac{400}{480}$

Step 4.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{400}{480}$

Step 4.5.3

Simplify the right side.

Tap for more steps...

Step 4.5.3.1

Cancel the common factor of $400$ and $480$ .

Tap for more steps...

Step 4.5.3.1.1

Factor $80$ out of $400$ .

$x = \frac{80 (5)}{480}$

Step 4.5.3.1.2

Cancel the common factors.

Tap for more steps...

Step 4.5.3.1.2.1

Factor $80$ out of $480$ .

$x = \frac{80 \cdot 5}{80 \cdot 6}$

Step 4.5.3.1.2.2

Cancel the common factor.

$x = \frac{80 \cdot 5}{80 \cdot 6}$

Step 4.5.3.1.2.3

Rewrite the expression.

$x = \frac{5}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{6}$

Decimal Form:

$x = 0.8\overline{3}$