Martin is considering the expressions 1/2(7x+48) and -(1/2x-3). he wants to know if one expression is greater than the other for all values of x. which statement about the relationship between the expressions is true?

The correct answer is that the expressions are equal when x=-5.25; when x>-5.25, the first expression is greater; and when x<-5.25, the first expression is smaller.

Explanation:
We set the expressions equal to one another first:
1/2(7x+48)=-(1/2x-3).

Using the distributive property on both sides, we have
(1/2)*7x+(1/2)*48=-1/2x- -3
7/2x+24=-1/2x+3.

To solve this, we can add 1/2x to both sides:
7/2x+24+1/2x=-1/2x+3+1/2x
8/2x+24=3
4x+24=3.

Subtract 24 from both sides:
4x+24-24=3-24
4x=-21.

Divide both sides by 4:
4x/4=-21/4
x=-21/4=-5.25.

This is the point where the two expressions are equal. If we were to repeat this process, except use a > symbol rather than =, we would have the solution x>-5.25; this means when x>-5.25, the first expression is larger.

Similarly, we can replace the equals with a less than, and end up with x<-5.25, which means when x is below this number, the first expression is smaller than the second.