All Junior Cert Mathematics posts
• #### Inequalities allixce

could anyone show me how to do the inequalities with fractions like on the 2013 paper 1 question 11 (a) ? Thank you :)

1. #### eltighe

okay so what you want to do is have x by itself in the middle. That means u have to cancel out the 1/2 and the -3 but you have to do this to the other numbers too.

-2 +3 ≤ 1/2x -3 +3 ≤ 1 +3

now you have gotten rid of the -3 in the middle.

1 ≤ 1/2x ≤ 4

now to have x by itself you have to divide each number by a half

1 ÷ 1/2 ≤ 1/2x ÷ 1/2 ≤ 4 ÷ 1/2

now x is by itself

2≤ x ≤ 8

i hope this helped:)

2. #### studybuddy15

This is basically the same method as to eltighe but it is just presented differently. eltighe does everything at the same time but we were taught to split the inequality into 2 parts.

The question was:

– 2 ≤ 1/2x – 3 < 1

to split it you put the left side with the middle part and then the right side with the middle part so it'll look like this:

– 2 ≤ 1/2x – 3 1/2x – 3 < 1

now you factorise each side by putting x to one side and the numbers to the other:

1 ≤ 1/2x 1/2x < 4

1÷ 1/2 ≤ x x < 4÷1/2

2 ≤ x x < 8

When you are done you put the 2 half's together to make:

2≤ x ≤ 8

I hope this helped

3. #### studybuddy15

I'm sorry, i just noticed my explanation didn't turn out the way I want'd it to be. There is supposed to be a gap between the two sides to make them separate. It might be easier to see if you write it down on a piece of paper and to put a clear gap between the two sides--for example

– 2 ≤ 1/2x – 3,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 1/2x – 3 < 1

4. #### allixce

ah thats perfect, thank you both so much!:)