2 questions I want to verify

Question

which expression is equal to "three less than a number multiplied by six"?

I think it's 6x-3

Also

1*(3+7)=(1*3)+(1*7) is distributive.  I just want to verify

Answer 1

When explaining expressions, I always ask the question, “What did you start with?”

“three less than a number multiplied by 6” , implies that you started with 6x and then subtracted 3. This can be verified by asking the learner, “What is three less than ten?

Is it 10-3 or 3-10? Most will agree it is 10-3.

Answer 2

3 less than a number multiplied by 6

= 6x-3

or

it could mean 6(x-3) = 6x-18,

but go with 6x-3. It's more likely what is "correct"

still the English language can be ambiguous, and doesn't translate clearly into the more precise math. so

it's not certain

you're right on the distribution property

1x(3+7) = 1x3 +1x7 = 3+7 = 10

Answer 3

For the first question, we need to translate what each part means:

1. "3 less than..." - other ways of stating this are "something take away 3" or "something minus 3"
2. "a number multiplied by 6" - you don't know what number a number is, so we would use something to represent that unknown; a variable (for example x)

Now when you combine the two parts you get 6*x minus 3 or 6x - 3

For the second question you do exactly what you did: multiply what's on the outside by the first inner term, then multiply what's on on the outside by the second inner term, and so forth. Be mindful of negatives and exponents if applicable*

*example: -x(x-3) = (-x)(x) + (-x)(-3) = -x^2 + 3x

Answer 4

Both of your answers are correct!

To clarify your first equation for other readers:  "three less than a number" means the number minus 3, so    - 3 will be at the end of the equation.  "A number multiplied by 6" means the number times 6.  Choose any symbol to represent "a number."  Grace chose x as the symbol.  So, the expression becomes 6x - 3.

The 2nd equation is an example of using the distributive property to solve a problem. 
For 1*(3+7), you multiply 1 by the first term in the parentheses (1*3), then by the second term in the parentheses (1*7).  Put a plus sign between the two because there is a plus sign inside the parentheses.  So, 1*(3+7) = (1*3) + (1*7).  If there had been a minus sign inside the parentheses, there would be a minus sign between the two products.  1*(3-7) = (1*3) - (1*7)

Grace, it looks like you have a good handle on your math!

Answer 5

In an effort to connect your questions, 6x-3 could also be written as 3*(2x - 1) which equals (3*2x) - (3*1). Just something extra to think about. :)

Answer 6

Both of these are correct. Great Job!