Question

Martin is considering the expressions 12(7x+48) and −(12x−3)+4(x+5). He wants to know if one expression is greater than the other for all values of x. Show or explain how you found your answer to Part A. Enter your work or your explanation in the box provided.Write a new expression that always has a greater value than both of these expressions. Enter your expression in the box provided.

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

Explanation: