[tex]\huge\text{Answer:}[/tex]
Inequality number 1: x≥7
Inequality number 2: x<3
Inequality number 3: x≤-2
Inequality number 4: x≤7
[tex]\huge\text{Solution:}[/tex]
1. 3x+12-6x≤-9
3x-6x+12≤-9
Subtract the x's:
-3x+12≤-9
-3x≤-9-12
-3x≤-21
3x≥21
x≥7
2. x+5x-6<12
6x-6<12
Move 6 to the right, using the [tex]\bold{\underline{opposite ~operation}}[/tex]:
6x<12+6
6x<18
Now, divide both sides by 6:
x<3
3. 5(x+8)-7≤23
Use the Distributive Property:
5x+40-7≤23
5x+33≤23
5x≤23-33
5x≤-10
x≤-2
4. 4x-6≥6x-20
4x-6x≥-20+6
-2x≥-14
2x≤14
x≤7
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Note:
If we divide both sides of the inequality by a negative variable, we flip the inequality sign.
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Hope you find it helpful.
Feel free to ask if you have any doubts.
