Distributive Property. (Simplify) 17. 3(x-2)= 18. -2(4x+9)= 19 (1)/(2)(10x-13)= -(2)/(3)(x-9)=

Let's simplify each expression using the **distributive property**, which states that \( a(b + c) = ab + ac \).<br /><br />---<br /><br />### 17. \( 3(x - 2) \)<br />Distribute \( 3 \) to both terms inside the parentheses:<br />\[<br />3(x - 2) = 3 \cdot x - 3 \cdot 2<br />\]<br />\[<br />= 3x - 6<br />\]<br /><br />**Answer:** \( 3x - 6 \)<br /><br />---<br /><br />### 18. \( -2(4x + 9) \)<br />Distribute \( -2 \) to both terms inside the parentheses:<br />\[<br />-2(4x + 9) = -2 \cdot 4x + (-2 \cdot 9)<br />\]<br />\[<br />= -8x - 18<br />\]<br /><br />**Answer:** \( -8x - 18 \)<br /><br />---<br /><br />### 19. \( \frac{1}{2}(10x - 13) \)<br />Distribute \( \frac{1}{2} \) to both terms inside the parentheses:<br />\[<br />\frac{1}{2}(10x - 13) = \frac{1}{2} \cdot 10x - \frac{1}{2} \cdot 13<br />\]<br />\[<br />= 5x - \frac{13}{2}<br />\]<br /><br />**Answer:** \( 5x - \frac{13}{2} \)<br /><br />---<br /><br />### 20. \( -\frac{2}{3}(x - 9) \)<br />Distribute \( -\frac{2}{3} \) to both terms inside the parentheses:<br />\[<br />-\frac{2}{3}(x - 9) = -\frac{2}{3} \cdot x - \left(-\frac{2}{3} \cdot 9\right)<br />\]<br />\[<br />= -\frac{2}{3}x + 6<br />\]<br /><br />**Answer:** \( -\frac{2}{3}x + 6 \)<br /><br />--- <br /><br />### Final Answers:<br />17. \( 3x - 6 \) <br />18. \( -8x - 18 \) <br />19. \( 5x - \frac{13}{2} \) <br />20. \( -\frac{2}{3}x + 6 \)