Evaluate 2 3/5*x+3-2/3x-1

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

Convert $2 \frac{3}{5}$ to an improper fraction.

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

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

Add $2$ and $\frac{3}{5}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $2$ by $5$ .

$\frac{10 + 3}{5} \cdot x + 3 - \frac{2}{3} x - 1$

Add $10$ and $3$ .

$\frac{13}{5} \cdot x + 3 - \frac{2}{3} x - 1$

Simplify each term.

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Combine $\frac{13}{5}$ and $x$ .

$\frac{13 x}{5} + 3 - \frac{2}{3} x - 1$

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

$\frac{13 x}{5} + 3 - \frac{x \cdot 2}{3} - 1$

Move $2$ to the left of $x$ .

$\frac{13 x}{5} + 3 - \frac{2 x}{3} - 1$

To write $\frac{13 x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{13 x}{5} \cdot \frac{3}{3} - \frac{2 x}{3} + 3 - 1$

To write $- \frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{13 x}{5} \cdot \frac{3}{3} - \frac{2 x}{3} \cdot \frac{5}{5} + 3 - 1$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{13 x}{5}$ and $\frac{3}{3}$ .

$\frac{13 x \cdot 3}{5 \cdot 3} - \frac{2 x}{3} \cdot \frac{5}{5} + 3 - 1$

Multiply $5$ by $3$ .

$\frac{13 x \cdot 3}{15} - \frac{2 x}{3} \cdot \frac{5}{5} + 3 - 1$

Multiply $\frac{2 x}{3}$ and $\frac{5}{5}$ .

$\frac{13 x \cdot 3}{15} - \frac{2 x \cdot 5}{3 \cdot 5} + 3 - 1$

Multiply $3$ by $5$ .

$\frac{13 x \cdot 3}{15} - \frac{2 x \cdot 5}{15} + 3 - 1$

Combine the numerators over the common denominator.

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + 3 - 1$

Find the common denominator.

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Write $3$ as a fraction with denominator $1$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3}{1} - 1$

Multiply $\frac{3}{1}$ by $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3}{1} \cdot \frac{15}{15} - 1$

Multiply $\frac{3}{1}$ and $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} - 1$

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

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} + \frac{- 1}{1}$

Multiply $\frac{- 1}{1}$ by $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} + \frac{- 1}{1} \cdot \frac{15}{15}$

Multiply $\frac{- 1}{1}$ and $\frac{15}{15}$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5}{15} + \frac{3 \cdot 15}{15} + \frac{- 1 \cdot 15}{15}$

Combine fractions with similar denominators.

$\frac{13 x \cdot 3 - 2 x \cdot 5 + 3 \cdot 15 - 1 \cdot 15}{15}$

Simplify the expression.

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Multiply $3$ by $15$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5 + 45 - 1 \cdot 15}{15}$

Multiply $- 1$ by $15$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5 + 45 - 15}{15}$

Subtract $15$ from $45$ .

$\frac{13 x \cdot 3 - 2 x \cdot 5 + 30}{15}$

Multiply $3$ by $13$ .

$\frac{39 x - 2 x \cdot 5 + 30}{15}$

Multiply $5$ by $- 2$ .

$\frac{39 x - 10 x + 30}{15}$

Subtract $10 x$ from $39 x$ .

$\frac{29 x + 30}{15}$

Evaluate 2 3/5*x+3-2/3x-1

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