Inequalities / Interval notation

Find all values of x satisfying the inequalities. Present your answer using the interval notation and illustrate it with the help of the number axis.

Hey guys.

I just wanted to know if I'm on the right track with these questions.

a) (x - 1) (2x + 3) > 0

**answer: x > 1 , x > - 1.5 **

b) |7 + 2x| >/_ 3

**answer: x>/_ 3 (x is greater than or equal to 3)**

c) |2x - 7| </_ 3x - 10

**answer: x >/_ -2 or x >/_ -5 (x is greater than or equal to -2 or x is greater than or equal to -5)**

(Apologies for the greater than / equal to signs - I didn't know how to in put them. The underscore (_) represents the equal to sign)

Re: Inequalities / Interval notation

I'm just not sure about the interval notation and how you represent it on the number axis.

Re: Inequalities / Interval notation

type \leq for :

and

type \geq for :

link

Re: Inequalities / Interval notation

Two comments about part a. If x>1 it will be greater than -3/2 so that part of the answer is just x>1

Now use the fact that if both brackets are negative (that is <0) the product will be >0

Re: Inequalities / Interval notation

So its not x>-1.5 just x>1 ?

Re: Inequalities / Interval notation

Yes. Any value that is greater than 1 will also be greater than -1.5 so we don't need to write x greater than -1.5 as well as x greater than 1

Re: Inequalities / Interval notation

a) seems to be resolved

b) for this one please remember the rule or

following the rule

or

or

or are your solutions

c) similar situation but remember the rule