how do I set up "four times the sum of 4 and a number yields the difference between 24 and 6 times the number".

Question

I struggle with turning math word problems into algebraic expressions.

Answer 1

If x is the number,

then the "sum of 4 and a number" is 4 + x.

Four times that sum would be 4(4 + x).

That is one side of the equation we are going to write.

For the other side of the equation we start with "6 times the number" which would be 6x.

The word difference in the phrase "the difference between 24 and 6 times the number" is indicating subtraction.  

So we get 24 - 6x.

In this problem, yields if the word that is standing for the equal sign, so we have

4(4 + x) = 24 - 6x.

 

Now you can just solve that equation.

 

I am afraid I don't quite agree with Michael J's suggestion, because of the order of the subtraction, but "difference" is often confusing.  The difference between 5 and 3 is 2, and the difference between 3 and 5 is -2.

Answer 2

Let x = number

 

6x-24 = 4(x+4)