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I'm having a bit of trouble on equalities ith absoulute values and X. can you explain them to me with this problem?

 

l2/13X + 5/26l is less than or equal to 9/52

 

thanks!

Guest Mar 9, 2017
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3+0 Answers

 #1
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l (2/13)x + 5/26 l   ≤  9/52

 

We actually have two equations, here because  if   l a l   ≤  b     then either a ≤ b  or -a  ≤ b....so we have

 

(2/13)x  + 5/26  ≤  9/52     getting common denominators, we have

 

(8/52)x + 10/52 ≤ 9/52      multiplying throgh by 52 to clear the fractions, we have

 

8x + 10   ≤  9       subtract 10 from both sides

 

8x ≤ -1   divide both sides by 8

 

x ≤ -1/8

 

And the other solution is :

 

- [(2/13)x  + 5/26 ]  ≤  9/52     simplify

 

-(2/13)x - 5/26 ≤ 9/52  getting common denominators, we have

 

-(8/52)x - 10/52 ≤ 9/52      multiplying throgh by 52 to clear the fractions, we have

 

-8x - 10   ≤  9       add 10 to both sides

 

-8x ≤ 19   divide both sides by -8  and reverse the inequality sign

 

x ≥ -19/8

 

So...the solution  interval is    -19/8   ≤  x    ≤   -1/8

 

Here's the graph demonstrating this  : https://www.desmos.com/calculator/nckzdetuth

 

 

cool cool cool

CPhill  Mar 9, 2017
 #2
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ugh... this makes my head spin...

Guest Mar 9, 2017
 #3
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(10 hours later ) ok, I get it.

Guest Mar 10, 2017

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