[Wolfeden]

solve so that {x|? <= x <= ?}

[Clough]

Hi, Wolfeden!

Are you looking for direct answers to the problem, or for someone to come along and teach you how to come up with the correct answers yourself, please?

If the former is true, please click on the following link to read the announcement there.

https://www.askmehelpdesk.com/math-s...-b-u-font.html

Thanks!

[bluefairy_nebul]

In solving inequality problems, the main goal is to isolate X (the unknown variable) on one side.

1. You can add or subtract same number from both sides.

For example 5x-7<= -8
=>5x-7+7<=-8+7 (I want to isolate x)
=>5x<=-1
2. You can divide or multiply both sides by same number

5x/5<=-1/5
=>x<=-1/5
3. Dividing or multiplying both sides by a negative number reverses the inequality

(-1)x>=(-1/5)(-1)
=>-x>=1/5

Now solve your problem part by part-
1. 3x-6<=-1
2. 3x-6>=-17

x<=? X>=? So,{x|___ <= x <= ___}

[Unknown008]

Hm.. quite hard to get without the LaTeX...

I'll give one more example.

If



You can subtract 5 from all the three sides to give:





Then, you can divide everywhere by 2 to give:





So that'll be your answer. If you want to make sure that it's the right answer, try out one value of x (eg. 0, 1, or 2) into the initial inequality. You should get the value between 5 and 9 inclusive.

To go further, say you divide by a negative number... like -1





Let's see if that is still good... 0 is less than or equal to -x... but you know that from above, x is between 0 and 2, and if you let x = 1, for example, the equation is not true! Conversely, is not true either! What happened? Well, whenever you divide or multiply by a negative number, the > and < signs flip over, like this:



Now, that inequality is valid for the previous solution.