Question

a)Solve the inequation:

2x-5<x+1, where xN​

Answer 1

This is a compound inequality with an OR condition - so there are two conditions. This means that when we solve for x, it can either satisfy the first condition (the first inequality) OR the second condition (the second inequality), OR both.

Let's solve the first inequality for  

x

5<-5

First we add  

−5

to both sides of the inequality to get:

2x0

Then, we divide by  

2

on both sides of the inequality. This gives us:

x<0

Let's solve the second inequality for  

x

.

2x+2>4

First, we subtract  

2

on both sides of the inequality.

2x>2

Then, we divide by  

2

on both sides of the inequality.

x>1

So here are our solutions for  

x:x<0  OR  x>1  

This means that any values between 0 and 1 (inclusive) will not satisfy either inequality. There are no common values of x that satisfy BOTH inequalities, which may happen in other cases.

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