Martin is considering the expressions 1/2 (7x + 48) and - [1/2x - 3] + 4 (x + 5). He wants to know if one expression is greater than the other for all values of x. Write a new expression that always has a greater value than both of these expressions.

Part A

The first thing we must do for this case is to rewrite both expressions.

We have then:

1/2 (7x + 48) = (7/2) x + 24

- [1 / 2x - 3] + 4 (x + 5) = - (1/2) x + 3 + 4x + 20 = (7/2) x + 23

Answer:

We note that the first expression is greater than the second for all values of x.

Part B:

A new expression that is greater than both written expressions is:

(7/2) x + 25

For all values of x, this expression is always greater.

Answer:

(7/2) x + 25