Math Question-Expression

Question

What number must be in the blank in the expression 3(x+7)-__(2x+9) if the expression is the same for all the values of x?

Answer 1

Hello Isabella,

You are looking for an expression that will be the same regardless of the value of x. So this expression needs to NOT depend on x. In other words, the final expression should only have numbers in it, NO x variables.

Let's call that number a and solve for it:

3(x+7)-_a_(2x+9) = 3x+ 21 - a*2x - a*9

Grouping like terms: 3x - 2ax + 21 - 9a

Again, this x-variable needs to be eliminated, that means: 3x - 2ax = 0 ---> 3x = 2ax ---> 3 = 2a ----> a = 3/2

check: 3(x+7)-(3/2)*(2x+9) = 3x+ 21 - (3/2)*(2) - (3/2)*9 = 3x+21 - 3x - 27/2 = 21-27/2 = 15/2, which, as you can see, only has a constant, NO x-variable. x could equal 1,000 or -4 and the answer will be the same.

So you need 3/2 in the expression 3(x+7)-__(2x+9) for that expression to be the same for all x-values.

Cheers.