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

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

Simplify the left side.

Simplify $\frac{3}{4} x - 1 \frac{5}{8}$ .

Convert $1 \frac{5}{8}$ to an improper fraction.

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

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

Add $1$ and $\frac{5}{8}$ .

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

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

Combine the numerators over the common denominator.

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

Add $8$ and $5$ .

$\frac{3}{4} x - \frac{13}{8} = 2 \frac{3}{4}$

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

$\frac{3 x}{4} - \frac{13}{8} = 2 \frac{3}{4}$

Simplify the right side.

Convert $2 \frac{3}{4}$ to an improper fraction.

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

$\frac{3 x}{4} - \frac{13}{8} = 2 + \frac{3}{4}$

Add $2$ and $\frac{3}{4}$ .

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

$\frac{3 x}{4} - \frac{13}{8} = 2 \cdot \frac{4}{4} + \frac{3}{4}$

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

$\frac{3 x}{4} - \frac{13}{8} = \frac{2 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} - \frac{13}{8} = \frac{2 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{3 x}{4} - \frac{13}{8} = \frac{8 + 3}{4}$

Add $8$ and $3$ .

$\frac{3 x}{4} - \frac{13}{8} = \frac{11}{4}$

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

Add $\frac{13}{8}$ to both sides of the equation.

$\frac{3 x}{4} = \frac{11}{4} + \frac{13}{8}$

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

$\frac{3 x}{4} = \frac{11}{4} \cdot \frac{2}{2} + \frac{13}{8}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{4}$ by $\frac{2}{2}$ .

$\frac{3 x}{4} = \frac{11 \cdot 2}{4 \cdot 2} + \frac{13}{8}$

Multiply $4$ by $2$ .

$\frac{3 x}{4} = \frac{11 \cdot 2}{8} + \frac{13}{8}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} = \frac{11 \cdot 2 + 13}{8}$

Simplify the numerator.

Multiply $11$ by $2$ .

$\frac{3 x}{4} = \frac{22 + 13}{8}$

Add $22$ and $13$ .

$\frac{3 x}{4} = \frac{35}{8}$

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

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{35}{8}$

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.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot \frac{35}{8}$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{35}{8}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot \frac{35}{8}$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot \frac{35}{8}$

Rewrite the expression.

$x = \frac{4}{3} \cdot \frac{35}{8}$

Simplify the right side.

Simplify $\frac{4}{3} \cdot \frac{35}{8}$ .

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$x = \frac{4}{3} \cdot \frac{35}{4 (2)}$

Cancel the common factor.

$x = \frac{4}{3} \cdot \frac{35}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{35}{2}$

Multiply $\frac{1}{3}$ by $\frac{35}{2}$ .

$x = \frac{35}{3 \cdot 2}$

Multiply $3$ by $2$ .

$x = \frac{35}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{35}{6}$

Decimal Form:

$x = 5.8\overline{3}$

Mixed Number Form:

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

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

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