Solve for x 4 1/2-5 1/3÷(20x-14 2/3)=1 5/6

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

Simplify the left side.

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $2$ .

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

Add $8$ and $1$ .

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $3$ .

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

Add $15$ and $1$ .

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $14$ by $3$ .

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

Add $42$ and $2$ .

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

Simplify each term.

Rewrite the division as a fraction.

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

Multiply the numerator by the reciprocal of the denominator.

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

Simplify the denominator.

To write $20 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $20 x$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $4$ out of $20 x \cdot 3 - 44$ .

Factor $4$ out of $20 x \cdot 3$ .

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

Factor $4$ out of $- 44$ .

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

Factor $4$ out of $4 (5 x \cdot 3) + 4 (- 11)$ .

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

Multiply $3$ by $5$ .

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

Multiply the numerator by the reciprocal of the denominator.

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

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

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

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $15$ by $9$ .

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

Multiply $9$ by $- 11$ .

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

Multiply $- 4$ by $2$ .

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

Subtract $8$ from $- 99$ .

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

Simplify the right side.

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $6$ and $5$ .

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

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.

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

Solve the equation for $x$ .

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

Start simplifying.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $6$ by $135$ .

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

Multiply $- 107$ by $6$ .

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

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

Apply the distributive property.

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

Multiply.

Multiply $15$ by $2$ .

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

Multiply $2$ by $- 11$ .

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

Apply the distributive property.

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

Multiply.

Multiply $11$ by $30$ .

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

Multiply $- 22$ by $11$ .

$810 x - 642 = 330 x - 242$

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

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

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

Subtract $330 x$ from $810 x$ .

$480 x - 642 = - 242$

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

Add $642$ to both sides of the equation.

$480 x = - 242 + 642$

Add $- 242$ and $642$ .

$480 x = 400$

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

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

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

Simplify the left side.

Cancel the common factor of $480$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

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

Factor $80$ out of $400$ .

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

Cancel the common factors.

Factor $80$ out of $480$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Exclude the solutions that do not make $4 \frac{1}{2} - 5 \frac{1}{3} \div (20 x - 14 \frac{2}{3}) = 1 \frac{5}{6}$ true.

$No solution$

Solve for x 4 1/2-5 1/3÷(20x-14 2/3)=1 5/6

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