Question

solve following inequality and write in interval notation: l3x-9l is > or = to 6

Answer 1

\[\left| 3x-9 \right| \ge 6\]

Answer 2

\[\left| 3x - 9 \right|\ge 6\]

Add 9 to both sides

\[\left| 3x \right|\ge 15\]

Divide both sides by 3

\[\left| x \right|\ge 5\]

Answer 3

@mando06 do you get it? :P

Answer 4

what about interval notation

Answer 5

Omg I'm stupid, this is absolute value haha

Answer 6

So this type of absolute value inequality is called a disjunction.

\[\left| x \right|> y\]

\[\left| x \right| \ge y\]

These are disjunctions

Answer 7

Disjunctions = or

The way you set up this problem is simple.

|3x−9|≥6

Convert to

\[|3x−9|≥6 or |3x−9|\le -6\]

Answer 8

"or" is not a variable nor a set of variables, it's merely a divider that states that this equation is a disjunction.

Answer 9

*inequality

Answer 10

So now just solve both inequalities similar to how I did it before

Answer 11

|3x−9|≥6

Add 9 to both sides

|3x|≥15

Divide both sides by 3

|x|≥5


|3x−9|≤−6

Add 9 to both sides

|3x|≤ 3

Divide both sides by 3

|x|≤ 1

Answer 12

@mando06

Answer 13

\[\left| x \right| \ge 5 or \left| x \right| \le 1\]