Simplify 3/5x+19-3/20x-7

$\frac{3}{5} x + 19 - \frac{3}{20} x - 7$

Step 1

Simplify each term.

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

$\frac{3 x}{5} + 19 - \frac{3}{20} x - 7$

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

$\frac{3 x}{5} + 19 - \frac{x \cdot 3}{20} - 7$

Move $3$ to the left of $x$ .

$\frac{3 x}{5} + 19 - \frac{3 x}{20} - 7$

Step 2

To write $\frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{5} \cdot \frac{4}{4} - \frac{3 x}{20} + 19 - 7$

Step 3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{5}$ by $\frac{4}{4}$ .

$\frac{3 x \cdot 4}{5 \cdot 4} - \frac{3 x}{20} + 19 - 7$

Multiply $5$ by $4$ .

$\frac{3 x \cdot 4}{20} - \frac{3 x}{20} + 19 - 7$

Step 4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 4 - 3 x}{20} + 19 - 7$

Step 5

Find the common denominator.

Write $19$ as a fraction with denominator $1$ .

$\frac{3 x \cdot 4 - 3 x}{20} + \frac{19}{1} - 7$

Multiply $\frac{19}{1}$ by $\frac{20}{20}$ .

$\frac{3 x \cdot 4 - 3 x}{20} + \frac{19}{1} \cdot \frac{20}{20} - 7$

Multiply $\frac{19}{1}$ by $\frac{20}{20}$ .

$\frac{3 x \cdot 4 - 3 x}{20} + \frac{19 \cdot 20}{20} - 7$

Write $- 7$ as a fraction with denominator $1$ .

$\frac{3 x \cdot 4 - 3 x}{20} + \frac{19 \cdot 20}{20} + \frac{- 7}{1}$

Multiply $\frac{- 7}{1}$ by $\frac{20}{20}$ .

$\frac{3 x \cdot 4 - 3 x}{20} + \frac{19 \cdot 20}{20} + \frac{- 7}{1} \cdot \frac{20}{20}$

Multiply $\frac{- 7}{1}$ by $\frac{20}{20}$ .

$\frac{3 x \cdot 4 - 3 x}{20} + \frac{19 \cdot 20}{20} + \frac{- 7 \cdot 20}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 x \cdot 4 - 3 x + 19 \cdot 20 - 7 \cdot 20}{20}$

Step 7

Simplify each term.

Multiply $4$ by $3$ .

$\frac{12 x - 3 x + 19 \cdot 20 - 7 \cdot 20}{20}$

Multiply $19$ by $20$ .

$\frac{12 x - 3 x + 380 - 7 \cdot 20}{20}$

Multiply $- 7$ by $20$ .

$\frac{12 x - 3 x + 380 - 140}{20}$

Step 8

Simplify terms.

Subtract $3 x$ from $12 x$ .

$\frac{9 x + 380 - 140}{20}$

Subtract $140$ from $380$ .

$\frac{9 x + 240}{20}$

Factor $3$ out of $9 x + 240$ .

Factor $3$ out of $9 x$ .

$\frac{3 (3 x) + 240}{20}$

Factor $3$ out of $240$ .

$\frac{3 (3 x) + 3 (80)}{20}$

Factor $3$ out of $3 (3 x) + 3 (80)$ .

$\frac{3 (3 x + 80)}{20}$

Simplify 3/5x+19-3/20x-7

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