Answer: The simplified expression is: " [tex]3x + 5[/tex] " .
______________________________
Step-by-step explanation:
______________________________
Given the expression:
______________________________
" One-half (8 x + 4) + one-third (9 minus 3x) " ;
We can rewrite that as:
[tex]\frac{1}{2}[/tex] [tex](8x+4) + \frac{1}{3}(9-3x)[/tex]
Now, let us simplify the expression:
Start with:
[tex]\frac{1}{2}(8x+4)[/tex] ;
Note the "distributive property" of multiplication:
a(b + c) = ab + ac ;
Likewise:
[tex]\frac{1}{2}{(8x +4) = (\frac{1}{2})8x + (\frac{1}{2})4=\frac{8}{2}x +\frac{4}{2} =4x +2[/tex] ; '
Now continue with the remaining part of the expression:
[tex]+\frac{1}{3}(9-3x)[/tex] ;
Again, use the "distributive property" of multiplication:
a(b + c) = ab + ac ;
[tex]+\frac{1}{3}(9-3x)= (\frac{1}{3})9+(\frac{1}{3})(-3x)=\frac{9}{3}+(-\frac{3}{3}x)=3+(-1x);[/tex]
= 3 − 1x ;
= 3 − x ;
________________________________________
Now, combine both terms within the expression; to simplify the expression:
[tex](4x + 2) + (3 -x)[/tex] ;
Rewrite as:
[tex]4x + 2 + 3 - x[/tex] ;
Now, combine the "like terms":
[tex]^+4x -x = 4x -1x = 3x[/tex] ;
[tex]^+2 +3 = 5[/tex] ;
The simplified expression is: " [tex]3x + 5[/tex] " .
________________________________________
Hope this is helpful to you! Best wishes!
_________________________________________
