Inequalities

I need help with understanding inequalities. :mad:

7 (x-2) < -5
x < ________

I dont understand the concept.

I am curious. Are you a student? If yes, you are now on Inequalities in one of your Math subjects? If yes again, your teacher doesn't explain inequalities enough for you to understand them yet?
You are using textbook that has this chapter on inequalities? You read that textbook about inequalities?

Questions above are for your not understanding the concept of inequalities.
You have a teacher, you have a textbook. Each of those should/could make you understand inequalities.
Then we have internet, the Web. Search for "math, inequality".

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Inequality is like equation. Or, treat inequality like it were an equation only. (I hope you know/understand equations.) Do whatever you do in an inequality as you would in an equation. What you do on one side you do it also on the other side of the equation/inequality.
The biggest difference is that in inequalities, when you multiply or divide both sides by a negative number, you have to reverse the sense of the inequality. From > to <, or, from < to >, as the case may be.
In equations, that cannot be done because = is = however you reverse it.

7 (x-2) < -5 ---------(i)

Let us say (i) is just an equation, so,
7 (x-2) = -5
(x-2) = -5/7
x = -5/7 +2
x = (-5 +2*7)/7
x = 9/7 --------------***

Now we do (i),
7 (x-2) < -5
(x-2) < -5/7
x < -5/7 +2
x < (-5 +2*7)/7
x < 9/7 ----------answer

See?

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The reversings.

Say, 2 -3x > 4
So,
-3x > 4 -2
-3x > 2
Divide both sides by -3, so you have to reverse the > into <,
x < 2/(-3)
x < -3/2

See?

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Edit one day after:

2/(-3) is -2/3, not -3/2. Zeez.

Im in online homeschool and literally teach myself.

Thankyou for the help...I kinda forgot how to do this, but know I remember. :D