Solve for x 8 3/5=3/4x-5 1/2

$8 \frac{3}{5} = \frac{3}{4} x - 5 \frac{1}{2}$

Simplify the left side.

Convert $8 \frac{3}{5}$ to an improper fraction.

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

$8 + \frac{3}{5} = \frac{3}{4} x - 5 \frac{1}{2}$

Add $8$ and $\frac{3}{5}$ .

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 \cdot \frac{5}{5} + \frac{3}{5} = \frac{3}{4} x - 5 \frac{1}{2}$

Combine $8$ and $\frac{5}{5}$ .

$\frac{8 \cdot 5}{5} + \frac{3}{5} = \frac{3}{4} x - 5 \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 5 + 3}{5} = \frac{3}{4} x - 5 \frac{1}{2}$

Simplify the numerator.

Multiply $8$ by $5$ .

$\frac{40 + 3}{5} = \frac{3}{4} x - 5 \frac{1}{2}$

Add $40$ and $3$ .

$\frac{43}{5} = \frac{3}{4} x - 5 \frac{1}{2}$

Simplify the right side.

Simplify $\frac{3}{4} x - 5 \frac{1}{2}$ .

Convert $5 \frac{1}{2}$ to an improper fraction.

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

$\frac{43}{5} = \frac{3}{4} x - (5 + \frac{1}{2})$

Add $5$ and $\frac{1}{2}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{43}{5} = \frac{3}{4} x - (5 \cdot \frac{2}{2} + \frac{1}{2})$

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

$\frac{43}{5} = \frac{3}{4} x - (\frac{5 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{43}{5} = \frac{3}{4} x - \frac{5 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{43}{5} = \frac{3}{4} x - \frac{10 + 1}{2}$

Add $10$ and $1$ .

$\frac{43}{5} = \frac{3}{4} x - \frac{11}{2}$

Combine $\frac{3}{4}$ and $x$ .

$\frac{43}{5} = \frac{3 x}{4} - \frac{11}{2}$

Rewrite the equation as $\frac{3 x}{4} - \frac{11}{2} = \frac{43}{5}$ .

$\frac{3 x}{4} - \frac{11}{2} = \frac{43}{5}$

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

Add $\frac{11}{2}$ to both sides of the equation.

$\frac{3 x}{4} = \frac{43}{5} + \frac{11}{2}$

To write $\frac{43}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} = \frac{43}{5} \cdot \frac{2}{2} + \frac{11}{2}$

To write $\frac{11}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{4} = \frac{43}{5} \cdot \frac{2}{2} + \frac{11}{2} \cdot \frac{5}{5}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{43}{5}$ by $\frac{2}{2}$ .

$\frac{3 x}{4} = \frac{43 \cdot 2}{5 \cdot 2} + \frac{11}{2} \cdot \frac{5}{5}$

Multiply $5$ by $2$ .

$\frac{3 x}{4} = \frac{43 \cdot 2}{10} + \frac{11}{2} \cdot \frac{5}{5}$

Multiply $\frac{11}{2}$ by $\frac{5}{5}$ .

$\frac{3 x}{4} = \frac{43 \cdot 2}{10} + \frac{11 \cdot 5}{2 \cdot 5}$

Multiply $2$ by $5$ .

$\frac{3 x}{4} = \frac{43 \cdot 2}{10} + \frac{11 \cdot 5}{10}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} = \frac{43 \cdot 2 + 11 \cdot 5}{10}$

Simplify the numerator.

Multiply $43$ by $2$ .

$\frac{3 x}{4} = \frac{86 + 11 \cdot 5}{10}$

Multiply $11$ by $5$ .

$\frac{3 x}{4} = \frac{86 + 55}{10}$

Add $86$ and $55$ .

$\frac{3 x}{4} = \frac{141}{10}$

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{141}{10}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{141}{10}$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{141}{10}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot \frac{141}{10}$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{141}{10}$

Rewrite the expression.

$x = \frac{4}{3} \cdot \frac{141}{10}$

Simplify the right side.

Simplify $\frac{4}{3} \cdot \frac{141}{10}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{3} \cdot \frac{141}{10}$

Factor $2$ out of $10$ .

$x = \frac{2 \cdot 2}{3} \cdot \frac{141}{2 \cdot 5}$

Cancel the common factor.

$x = \frac{2 \cdot 2}{3} \cdot \frac{141}{2 \cdot 5}$

Rewrite the expression.

$x = \frac{2}{3} \cdot \frac{141}{5}$

Cancel the common factor of $3$ .

Factor $3$ out of $141$ .

$x = \frac{2}{3} \cdot \frac{3 (47)}{5}$

Cancel the common factor.

$x = \frac{2}{3} \cdot \frac{3 \cdot 47}{5}$

Rewrite the expression.

$x = 2 (\frac{47}{5})$

Combine $2$ and $\frac{47}{5}$ .

$x = \frac{2 \cdot 47}{5}$

Multiply $2$ by $47$ .

$x = \frac{94}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{94}{5}$

Decimal Form:

$x = 18.8$

Mixed Number Form:

$x = 18 \frac{4}{5}$

Solve for x 8 3/5=3/4x-5 1/2

Related Questions

Support LCMGCF.com by disabling your adblocker.