Solve for x 1 1/2x=9 9/20

$1 \frac{1}{2} x = 9 \frac{9}{20}$

Simplify the left side.

Simplify $1 \frac{1}{2} x$ .

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

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

$(1 + \frac{1}{2}) x = 9 \frac{9}{20}$

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

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

$(\frac{2}{2} + \frac{1}{2}) x = 9 \frac{9}{20}$

Combine the numerators over the common denominator.

$\frac{2 + 1}{2} x = 9 \frac{9}{20}$

Add $2$ and $1$ .

$\frac{3}{2} x = 9 \frac{9}{20}$

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

$\frac{3 x}{2} = 9 \frac{9}{20}$

Simplify the right side.

Convert $9 \frac{9}{20}$ to an improper fraction.

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

$\frac{3 x}{2} = 9 + \frac{9}{20}$

Add $9$ and $\frac{9}{20}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{3 x}{2} = 9 \cdot \frac{20}{20} + \frac{9}{20}$

Combine $9$ and $\frac{20}{20}$ .

$\frac{3 x}{2} = \frac{9 \cdot 20}{20} + \frac{9}{20}$

Combine the numerators over the common denominator.

$\frac{3 x}{2} = \frac{9 \cdot 20 + 9}{20}$

Simplify the numerator.

Multiply $9$ by $20$ .

$\frac{3 x}{2} = \frac{180 + 9}{20}$

Add $180$ and $9$ .

$\frac{3 x}{2} = \frac{189}{20}$

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot \frac{189}{20}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot \frac{189}{20}$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{189}{20}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot \frac{189}{20}$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot \frac{189}{20}$

Rewrite the expression.

$x = \frac{2}{3} \cdot \frac{189}{20}$

Simplify the right side.

Simplify $\frac{2}{3} \cdot \frac{189}{20}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $20$ .

$x = \frac{2}{3} \cdot \frac{189}{2 (10)}$

Cancel the common factor.

$x = \frac{2}{3} \cdot \frac{189}{2 \cdot 10}$

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{189}{10}$

Cancel the common factor of $3$ .

Factor $3$ out of $189$ .

$x = \frac{1}{3} \cdot \frac{3 (63)}{10}$

Cancel the common factor.

$x = \frac{1}{3} \cdot \frac{3 \cdot 63}{10}$

Rewrite the expression.

$x = \frac{63}{10}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{63}{10}$

Decimal Form:

$x = 6.3$

Mixed Number Form:

$x = 6 \frac{3}{10}$

Solve for x 1 1/2x=9 9/20

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