Question: 2x vs. y+2

I divided both sides by 2 and compared as follows.

Quantity A: 2x/2 Quantity B: (y+2)/2
Quantity A: x Quantity B: y/2 + 1

x < y/2 +1

Given that - X<Y/2, we can say => 2x<y
=> 2x A y+2 B
When 2x is greater than y, y+2 is greater than y,
Then y+2 is greater than 2x.

SO B is greater.

How about this conclusion Brent?

in the case of -y 2xgreater than y , here is not mentioned how much greater, that means might be equal or greater than answer d. it's right?

After watching you manipulate inequalities in ways that seem VERY simple once you do so, I clearly need to try to use number properties, etc., more often! Sheesh.

That having been said:

1. Manipulate the *given* info one step further than was done in the video:

Given info:

x < y/2
(multiply both sides by 2):
2x < y
(subtract y from both):
2x-y < 0
That is, (2x-y) is negative.

2. Now manipulate the Quantities. Given:

Qty A: 2x
Qty B: y+2

3. Subtract y from both to get:

Qty A: 2x-y
Qty B: 2

4. We know that 2x-y is negative. (Above, 2x-y<0), so we have:

Qty A: something NEGATIVE
Qty B: 2 (= POSITIVE)

Qty B is greater.

given x < y/2 (x2 both sides) to get 2x < y since 2 is +ve and doesn't change the inequality sign. we can now see that 2x < y so obviously 2x < y + 2. cheers