Gin L.
asked • 09/12/20−4|2x − 7| < 1 Can you show me the steps
Mark M. answered • 09/12/20
Mathematics Teacher - NCLB Highly Qualified
-4|2x - 7| < 1
|2x - 7| > -0,25
Assuming 2x - 7 > 0
2x - 7 > -0.25
2x > 6.75
x > 3.375
Assuming 2x - 7 < 0
-(2x - 7) > -0.25
2x - 7 < 0.25
2x < 7.25
x < 3.625
Raymond B. answered • 09/12/20
Math, microeconomics or criminal justice
Multiply by -1/4, that reverses the inequality
to get
absolute value of (2x-7) > -1/4
The absolute value of anything is always positive and greater than -1/4
x can be any real number, because 2x-7 can be any real number
-infinity < x < + infinity
are you sure you copied this problem correctly?
Mark M.
A standard process exists for solving inequalities with absolute values.09/12/20
Alex E.
Mark’s answer is correct. It’s an or statement x>3.375 or x< 3.625 is equivalent to all real numbers.09/12/20
Alex E.
Your path to the solution works as well though and to me is a bit more clever while Mark’s way is a good example for how to work the problem in general. If the student had the abs greater than a positive value, they would know how to approach the situation from Mark’s example. Cool part about math to me is seeing different paths to the solution.09/12/20
Alex E.
Not sure what you mean by I might be confusing and or with inclusive exclusive. However, |x|>a is equivalent to x>a OR x<-a. Im not going to write a proof for it, but if you think I don’t know what I’m talking about, I pulled out an old text that you can reference. Check Blitzer Algebra and Trigonometry 4e Instructor’s Edition p.183. If you need help understanding how to simplify an OR statement, here you can draw a line graph and see that Mark’s solution is the entire number line, but if you would like an additional reference for this let me know. However, I stand by my approval of Mark’s solution we’ll besides the fact that it simplifies to all real numbers.09/12/20
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X=4 is in the solution region that Mark obtained; every real number is. He just didn’t explicitly state that x>3.375 or x>3.625 is equivalent to all real numbers.09/12/20