Question

One-half (8 x + 4) + one-third (9 minus 3 x)

Answer 1

Answer:

3x + 5.

Step-by-step explanation:

factor out 1/6 (1/2 • 1/3)

distribute the 3 from the paranthesis

1/6 (3(8x + 4) + 2(9-3x))

1/6(24x + 12 + 2(9-3x))

distribute 2 through parentheses

1/6(24x+12+18-6x)

collect like terms:

1/6(18x + 12 + 18) > 1/6(18x +30)

factor out 6

1/6 • 6(3x+5)

reduce with GCF (6)

3x + 5

Answer 2

Answer:  The simplified expression is:  " $3x + 5$ " .

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Step-by-step explanation:

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Given the expression:

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" One-half (8 x + 4) + one-third (9 minus 3x) "  ;

We can rewrite that as:

$\frac{1}{2}$ $(8x+4) + \frac{1}{3}(9-3x)$

Now, let us simplify the expression:

Start with:

$\frac{1}{2}(8x+4)$ ;

Note the "distributive property" of multiplication:

  a(b + c)  = ab + ac ;

Likewise:

$\frac{1}{2}{(8x +4) = (\frac{1}{2})8x + (\frac{1}{2})4=\frac{8}{2}x +\frac{4}{2} =4x +2$ ;  '

Now continue with the remaining part of the expression:

$+\frac{1}{3}(9-3x)$ ;

Again, use the "distributive property" of multiplication:

     a(b + c)  = ab + ac ;

$+\frac{1}{3}(9-3x)= (\frac{1}{3})9+(\frac{1}{3})(-3x)=\frac{9}{3}+(-\frac{3}{3}x)=3+(-1x);$

                                                                          =  3 − 1x ;

                                                                          =  3 − x  ;

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Now, combine both terms within the expression; to simplify the expression:  

   $(4x + 2) + (3 -x)$ ;

Rewrite as:

   $4x + 2 + 3 - x$ ;

Now, combine the "like terms":

  $^+4x -x = 4x -1x = 3x$ ;

  $^+2 +3 = 5$  ;

The simplified expression is:  " $3x + 5$ " .

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Hope this is helpful to you!  Best wishes!

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