# Thread: Inequlaities etc. for tomorrow!!!!!!!

1. ## Inequlaities etc. for tomorrow!!!!!!!

Hi, i'm a new member who really needs help. We've had a supply teacher for a while who was terrible at teaching us. Now the real teacher is back (very scary) and wants homework on Inequalities in for tomorrow. I don't have a clue how to do them but she'll go mad if they're not done!

Please may i have some help?

The following questions i need help with:
Solve the following linear inequalities:
1a. x+3<8
d.4x-5<7
g.x+3 over 2 <8
j.2(x-3)<14
m.3x+1 more than or equal to 2x-5
p.3x+2 more than or equal to x+3

Thankyou.

2. Originally Posted by awfulatmaths
...

Solve the following linear inequalities:
1a. x+3<8
d.4x-5<7
g.x+3 over 2 <8
j.2(x-3)<14
m.3x+1 more than or equal to 2x-5
p.3x+2 more than or equal to x+3

Thankyou.
Hello,

1. You solve inequalities in the same manner as you solve equations with a few exceptions:

a) If you mulitply/divide both sides of an inequality by a negative number you have to change the < sign into a > sign, and the > sign into a < sign.

to #1a:

$\displaystyle x+3<8~\iff~x<5$

to #d:

$\displaystyle 4x-5<7~\iff~4x<2~\iff~x<\frac12$

to #g: Do you mean:

$\displaystyle \frac{x+3}{2}<8$ ? Mulitply by 2, subtract 3, done!

to #j: Expand the bracket, add 6, divide by 2
to #m: subtract 1, subtract 2x,
and the last one is intirely for you

3. I can't thank you enough earboth, i was extremely worried but thanks to you i now know not just the answers, but also how to work them out which i have shown in my exercise book. I was also able to do p-i wish you were my teacher.

Thanks a lot!