Question

wednesday
-2(3x+15)-3(3y+12)
6x - 9y - 6
\frac{1}{2}x - \frac{3}{4}y - \frac{3}{8} - \frac{9}{2}y + \frac{8}{9}x

Explanation:

Step1: Simplify \(-2(3x + 15)-3(3y + 12)\)

Use the distributive property \(a(b + c)=ab+ac\).
\(-2(3x)+(-2)(15)-3(3y)-3(12)= -6x - 30 - 9y - 36\)
Combine like terms: \(-6x - 9y + (-30 - 36)= -6x - 9y - 66\) (Note: There might be a typo in the original "6x - 9y - 6" as per correct expansion)

Step2: Simplify \(\frac{1}{2}x-\frac{3}{4}y-\frac{3}{8}-\frac{9}{2}y+\frac{8}{9}x\)

Combine \(x\)-terms: \(\frac{1}{2}x+\frac{8}{9}x=\frac{9}{18}x+\frac{16}{18}x=\frac{25}{18}x\)
Combine \(y\)-terms: \(-\frac{3}{4}y-\frac{9}{2}y=-\frac{3}{4}y-\frac{18}{4}y=-\frac{21}{4}y\)
Constant term: \(-\frac{3}{8}\)
So the simplified form is \(\frac{25}{18}x-\frac{21}{4}y-\frac{3}{8}\)

Answer:

• For \(-2(3x + 15)-3(3y + 12)\): \(\boldsymbol{-6x - 9y - 66}\) (corrected from the original's likely error)
• For \(\frac{1}{2}x-\frac{3}{4}y-\frac{3}{8}-\frac{9}{2}y+\frac{8}{9}x\): \(\boldsymbol{\frac{25}{18}x-\frac{21}{4}y-\frac{3}{8}}\)