how can i solve the inequality |3x-2| greater than or equal to 5

Question

tkhunny · Answer

Think about $|3x-2|$.  Where is that positive (or zero) and where is ti negative?  This will lead you to a solution.

anonymous · Answer

you should get 2 answers as well

tkhunny · Answer

Think about (3x−2). Where is that positive (or zero) and where is ti negative? This will lead you to a solution.

anonymous · Answer

$$|3x-2|\ge 5$$

anonymous · Answer

1st thing you need to do is remove the absolute value and set up the 2 equations

anonymous · Answer

what is the absolute value?

anonymous · Answer

the lines that the equation is inside of

anonymous · Answer

oh ok how do i remove that?

calculusxy · Answer

$$3x-2=5$$

calculusxy · Answer

Now solve for x. This is the same thing because you may be finding what could be EQUAL to 5.

anonymous · Answer

$$3x-2 \ge 5 $$ and  $$ 3x -2 \le -5 $$ 
is what you should get when removing absolute value
notice how the 1st equation is exactly the same as the one you wrote down without the absolute value and in the second one you switch the sign and change the number into negative (in this case)

anonymous · Answer

now all you need to do is solve for x

anonymous · Answer

let me know if you need to graph these as well

anonymous · Answer

ok so x it less than or equal to 1

anonymous · Answer

thank you choprak

anonymous · Answer

you should get 2 answers: $$x \le -1$$ and $$x \ge \frac{ 7 }{ 3 }$$

anonymous · Answer

anytime you see absolute value (the 2 lines) you should always get 2 answers :P