Foundations of Math - CH8 Inequalities & Absolute Values

[AlexandraO504]

Hello,

I am having some trouble reconciling two different answers within chapter 8 of the fundamentals of maths guide regarding inequalities and absolute values.

On the 'harder example' on page 340, the negative version of the inequality |y+3| <5 ends up saying:

-y < 8
y > -8

The above makes sense to me as you learn earlier on in the chapter that multiplying or dividing an inequality but a negative number results in a flip of the inequality sign. HOWEVER, there are multiple instances in the drill sets where the inequality sign doesn't flip despite multiplying by a negative. Take for example Q41 on page 348. The negative version of the inequality |x+3| < 1 ends up saying:

-x < 4
x < -4

I do not understand why it is that on this occasion the inequality doesn't flip whereas on the question two above the inequality does flip - in my mind, you are multiplying by -1 in both cases so the inequality sign should flip for both. Could you please tell me where I am going wrong?

Thanks!
Ally

[Sage Pearce-Higgins]

You're not going wrong at all. Unfortunately, despite our best efforts, occasional errors get past our editors. The line "x < -4" on p356 is one such example. However, you can see from the number line and expression below that we meant that x is between -4 and -2.

Please check here for other errors: https://www.manhattanprep.com/gmat/erra ... a-fom-6ed/