Question

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.

Answer 1

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