Simplify 1/2(3/5x-8)+7/4(2/5x+4)

$\frac{1}{2} (\frac{3}{5} x - 8) + \frac{7}{4} (\frac{2}{5} x + 4)$

Step 1

Simplify each term.

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

$\frac{1}{2} \cdot (\frac{3 x}{5} - 8) + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Apply the distributive property.

$\frac{1}{2} \cdot \frac{3 x}{5} + \frac{1}{2} \cdot - 8 + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Multiply $\frac{1}{2} \cdot \frac{3 x}{5}$ .

Multiply $\frac{1}{2}$ by $\frac{3 x}{5}$ .

$\frac{3 x}{2 \cdot 5} + \frac{1}{2} \cdot - 8 + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Multiply $2$ by $5$ .

$\frac{3 x}{10} + \frac{1}{2} \cdot - 8 + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Cancel the common factor of $2$ .

Factor $2$ out of $- 8$ .

$\frac{3 x}{10} + \frac{1}{2} \cdot (2 (- 4)) + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Cancel the common factor.

$\frac{3 x}{10} + \frac{1}{2} \cdot (2 \cdot - 4) + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Rewrite the expression.

$\frac{3 x}{10} - 4 + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

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

$\frac{3 x}{10} - 4 + \frac{7}{4} \cdot (\frac{2 x}{5} + 4)$

Apply the distributive property.

$\frac{3 x}{10} - 4 + \frac{7}{4} \cdot \frac{2 x}{5} + \frac{7}{4} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 x}{10} - 4 + \frac{7}{2 (2)} \cdot \frac{2 x}{5} + \frac{7}{4} \cdot 4$

Factor $2$ out of $2 x$ .

$\frac{3 x}{10} - 4 + \frac{7}{2 (2)} \cdot \frac{2 (x)}{5} + \frac{7}{4} \cdot 4$

Cancel the common factor.

$\frac{3 x}{10} - 4 + \frac{7}{2 \cdot 2} \cdot \frac{2 x}{5} + \frac{7}{4} \cdot 4$

Rewrite the expression.

$\frac{3 x}{10} - 4 + \frac{7}{2} \cdot \frac{x}{5} + \frac{7}{4} \cdot 4$

Multiply $\frac{7}{2}$ by $\frac{x}{5}$ .

$\frac{3 x}{10} - 4 + \frac{7 x}{2 \cdot 5} + \frac{7}{4} \cdot 4$

Multiply $2$ by $5$ .

$\frac{3 x}{10} - 4 + \frac{7 x}{10} + \frac{7}{4} \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 x}{10} - 4 + \frac{7 x}{10} + \frac{7}{4} \cdot 4$

Rewrite the expression.

$\frac{3 x}{10} - 4 + \frac{7 x}{10} + 7$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$- 4 + 7 + \frac{3 x + 7 x}{10}$

Add $3 x$ and $7 x$ .

$- 4 + 7 + \frac{10 x}{10}$

Cancel the common factor of $10$ .

Cancel the common factor.

$- 4 + 7 + \frac{10 x}{10}$

Divide $x$ by $1$ .

$- 4 + 7 + x$

Add $- 4$ and $7$ .

$3 + x$

Simplify 1/2(3/5x-8)+7/4(2/5x+4)

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