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

#1**+5 **

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

CPhill
Mar 9, 2017