Question

use the distributive property to simplify each variable expressi

1. (-\frac{2}{3}(9x - 18))
2. (\frac{8x - 5}{-8})

Explanation:

Step1: Apply Distributive Property

The distributive property states that \( a(b + c)=ab + ac \). For \( -\frac{2}{3}(9x - 18) \), we distribute \( -\frac{2}{3} \) to both \( 9x \) and \( - 18 \):
\( -\frac{2}{3}\times9x+(-\frac{2}{3})\times(-18) \)

Step2: Simplify Each Term

• For the first term: \( -\frac{2}{3}\times9x=-\frac{2\times9x}{3}=-6x \) (since \( 9\div3 = 3 \), and \( 2\times3 = 6 \), with the negative sign)
• For the second term: \( (-\frac{2}{3})\times(-18)=\frac{2\times18}{3}=12 \) (negative times negative is positive, and \( 18\div3 = 6 \), \( 2\times6 = 12 \))

Step3: Combine Terms

Combining the simplified terms, we get \( -6x + 12 \)

Answer:

\( -6x + 12 \)