Guide 3, 4th Ed.(4.0), Chapter 6, Pg 101, Question 6

[kpf102]

Hello- Can somebody please assist with this problem?

If |10y-4| > 7, and y < 1, which of the following could be y?
(a) -0.8
(b) -0.1
(c) 0.1
(d) 0
(e) 1

I'm having trouble understanding the significance of the "y < 1" inequality. The 1st inequality becomes (y > 1.1) & (y < -0.3) and we already have y < 1 for the simpler inequality.

(a) -0.8 is less than -0.3, understood and fits the question
(e) 1 is between the simpler inequality (y < 1) and 1.1, not part of the range, understood

However, can't (b) -0.1, (c) 0.1, and (d) 0 all be considered y since they are all less than 1? Is the "y < 1" inequality ignored because it expands the range of y instead of limiting it?

Thanks!

[itzdeepika]

|10y-4| > 7 means y>1.1 and y< -0.3
and y < 1
Since there is 'and' in between the |10y-4| > 7 and y< 1 we must consider the range of y which satisfies both the inequalities and in this case it is y< -0.3
Since -0.8 is less than -0.3 choice a is the answer.

[akhp77]

|10y-4| > 7
-7 > 10y-4 > 7
-3 > 10y > 11
-0.3 > y > 1.1
and y < 1 given

=>
y < -0.3
y could be -0.8
Ans A

[kpf102]

I believe that's the first time I see an inequalities question of this type. Thanks!

[Ben Ku]

Hello- Can somebody please assist with this problem?

If |10y-4| > 7, and y < 1, which of the following could be y?
(a) -0.8
(b) -0.1
(c) 0.1
(d) 0
(e) 1

I'm having trouble understanding the significance of the "y < 1" inequality. The 1st inequality becomes (y > 1.1) & (y < -0.3) and we already have y < 1 for the simpler inequality.

(a) -0.8 is less than -0.3, understood and fits the question
(e) 1 is between the simpler inequality (y < 1) and 1.1, not part of the range, understood

However, can't (b) -0.1, (c) 0.1, and (d) 0 all be considered y since they are all less than 1? Is the "y < 1" inequality ignored because it expands the range of y instead of limiting it?

Thanks!

Your solutions to the inequality is correct: either y > 1.1 or y < -0.3. If we consider the answer choices, only answer choice (a) satisfies this inequality.

When the word "AND" is used, that means BOTH conditions must be met. So (a) is the solution because it satisfies the inequality and it satisfies y < 1.

Answer choices (b), (c), and (d) are wrong because even though they satisfy y < 1, they don't meet the inequality.

Suppose we have answer choice (f) 2, this would also be wrong because although it satisfies the inequality, it does not satisfy y < 1.

So if you see the word AND, you need to make sure that BOTH conditions are met. If you see the word OR, then you just need to meet one of the conditions (not necessarily both).