Simplify 1/2(5(x+2)+4x)

$\frac{1}{2} (5 (x + 2) + 4 x)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{1}{2} \cdot (5 x + 5 \cdot 2 + 4 x)$

Multiply $5$ by $2$ .

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

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

Step 2

Simplify terms.

Add $5 x$ and $4 x$ .

$\frac{1}{2} \cdot (9 x + 10)$

Apply the distributive property.

$\frac{1}{2} (9 x) + \frac{1}{2} \cdot 10$

$\frac{1}{2} (9 x) + \frac{1}{2} \cdot 10$

Step 3

Multiply $\frac{1}{2} (9 x)$ .

Combine $9$ and $\frac{1}{2}$ .

$\frac{9}{2} x + \frac{1}{2} \cdot 10$

Combine $\frac{9}{2}$ and $x$ .

$\frac{9 x}{2} + \frac{1}{2} \cdot 10$

$\frac{9 x}{2} + \frac{1}{2} \cdot 10$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{9 x}{2} + \frac{1}{2} \cdot (2 (5))$

Cancel the common factor.

$\frac{9 x}{2} + \frac{1}{2} \cdot (2 \cdot 5)$

Rewrite the expression.

$\frac{9 x}{2} + 5$

$\frac{9 x}{2} + 5$

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