SOLUTION: Please help me with the following problems below trying to help my daughter don't want to show her the wrong way of how to solve these problems. HELP!!! 1. 3(4x)+ 4 if x=5

Remember the little rhyme:

" 'Side by side' means 'multiplied' "

The letters x is used so often for an unknown or variable quantity in 
algebra that the cross × is almost never used.  It looks too much like 
the letter x.  There are two ways to indicate multiplication in algebra.
Sometimes a dot • is placed between them to indicate multiplication.  
But the most common way is to place NOTHING between a number and a letter,
or between two letters.  Of course you can't write two numbers side-by-side,
for if you wrote 3 next to 4 it would look like the number 34. When two
numbers are to be multiplied one or both of them are enclosed in parentheses
and the parentheses is places next to what it is to be multiplied by.
The parentheses in the 1st example below keeps the 3 from being next to
the 4, otherwise it would look like 34x.  It might be easier if you use
the dot • to indicate multiplication.    

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1. 3(4x) + 4 if x=5 

That could be written using the dot:

  3•(4•x) + 4

Now we replace the x by 5 and we have:

  3•(4•5) + 4

We always do what's in parentheses first, so we do (4•5) and get 20.
so since we are using the dot we replace the (4•5) by (20)

  3•20 + 4

Multiplication is done before addition or subtraction so we replace 
the 3•20 by 60, and we have:

  60 + 4

And that is, of course, just

   64.

So on her paper she should write this:

3(4x) + 4 =
3•(4•x) + 4 =
3•(4•5) + 4 =
3•20 + 4 =
60 + 4 =
64

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2. 10(xy) if x=5 and y=6 

Write this:

10(xy) =
10•(x•y) =
10•(5•6) =
10•30 = 
300

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3. 6(3t + 4s) if t=4 and s=3

Write this:

6•(3•t + 4•s) =
6•(3•4 + 4•3) =   <--finish what's inside the parentheses first
6•(12 + 12) =        (do the multiplications before adding)
6•24 =
144

Edwin