SOLUTION: could you please help me solve this equation |2-3x|<(or equal) 5 I seem to have trouble with absolute values

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Question 1094170: could you please help me solve this equation
|2-3x|<(or equal) 5
I seem to have trouble with absolute values

Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
See this already started (but not fully solved) problem:

https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1094166.html
https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1094166.html

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve |2-3x| <= 5.
~~~~~~~~~~~~~~~~~~~~

|2-3x| <= 5.


Divide both sides by 3. You will get an equivalent inequality


abs%282%2F3-x%29 <= 5%2F3.


The solution set to this inequality is the set of those x that are remoted not farther than 5%2F3 units  from the point 2%2F3 on the number line, i.e

the set of x,  2%2F3+-+5%2F3 <= x <= 2%2F3%2B5%2F3,   or,  which is the same,

-1 <= x <= 7%2F3.


Answer.  The solution set is the segment  [-1,7%2F3] of the number line.


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
could you please help me solve this equation
|2-3x|<(or equal) 5
I seem to have trouble with absolute values
This is NOT an equation, but an INEQUALITY instead.
abs%282+-+3x%29+%3C=+5
2+-+3x+%3C=+5 OR 2+-+3x+%3E=+-+5
-+3x+%3C=+5+-+2 OR -+3x+%3E=+-+5+-+2
-+3x+%3C=+3 OR -+3x+%3E=+-+7
matrix%281%2C3%2C+x+%3E=+3%2F%28-+3%29%2C+or%2C+x+%3E=+-+1%29 OR matrix%281%2C3%2C+x+%3C=+%28-+7%29%2F%28-+3%29%2C+or%2C+x+%3C=+7%2F3%29
highlight_green%28-+1+%3C=+x+%3C=+7%2F3%29