D1

Hi,

I'm having trouble trying to put inequalities in context (Linear Programming chapter) and I am unsure how to approach them in a rational way.

For instance:

a) 4x ≦ y

b) x ≧ 5y

c) 'at most 5 times more x than y'

d) 'at least 2 times less x than y'


Thanks in advance.

I never did D1 at A-level, but this is too simple to resist

Hint:

y > 5x

means "5 times x [is] less than y"

"at most" is associated with less than or equal to

"at least" is associated with greater than or equal to.

Okay so for a) 4x ≦ y

4 times x is less than y

... so at most y is 4 times more than x?

No, you need "at least" in there

$4x \leq y \implies y \geq 4x$

a) 4x ≦ y --> y ≧ 4x

y is at least 4 times more than x

b) x ≧ 5y

x is at least 5 times more than y

c) 'at most 5 times more x than y'

x ≦ 5y

d) 'at least 2 times less x than y'

2x ≧ y

d) isn't quite right.

Take y=6 or something. What values of x do you need?