Question

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

Answer 1

3x + 5.

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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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:

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

Now, let us simplify the expression:

Start with:

`(1)/(2)(8x+4)` ;

Note the "distributive property" of multiplication:

a(b + c) = ab + ac ;

Likewise:

`(1)/(2){(8x +4) = ((1)/(2))8x + ((1)/(2))4=(8)/(2)x +(4)/(2) =4x +2` ; '

Now continue with the remaining part of the expression:

`+(1)/(3)(9-3x)` ;

Again, use the "distributive property" of multiplication:

a(b + c) = ab + ac ;

`+(1)/(3)(9-3x)= ((1)/(3))9+((1)/(3))(-3x)=(9)/(3)+(-(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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