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.

Question

A) 1/2 (7x + 48) is always equal to (1/2x - 3) +4 (x + 5)

B) 1/2 (7x + 48) is always less than (1/2x - 3) +4 (x + 5)

C) 1/2 (7x + 48) is always greater than (1/2x - 3) +4 (x + 5)

D) 1/2 (7x + 48) is sometimes less than sometimes greater than (1/2x - 3) +4 (x + 5)

Answer 1

(1/2)(7x+48) = (1/2)x -3 + 4(x+5)

(1/2)(7x+48) = x/2 -3 + 4(x+5)

7x/2 + 24 = 9x/2 +17

for x = 7 the expessions are equal

and unequal when x>7 or x<7

Left side is greater when x<7

Right side greater when x>7

D) is correct, if it implicitly says and sometimes they're equal