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!
+128454 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
