Menu Close

x-3-x-2-9-find-x-

Tinku Tara 0 Comments
Pin




Question Number 207718 by hardmath last updated on 24/May/24
∣x−3∣ + ∣x +2∣ = 9 find: x = ?
∣x−3∣+∣x+2∣=9find:x=?
Answered by TonyCWX08 last updated on 24/May/24
There are 4 possible cases. x−3+x+2=9 −(x−3)+x+2=9 x−3−(x+2)=9 −(x−3)−(x+2)=9 2x=10, x≥3,x≥−2 ∅ ∅ −2x=8,x<3,x<−2 x=5 x=−4
Thereare4possiblecases.x−3+x+2=9−(x−3)+x+2=9x−3−(x+2)=9−(x−3)−(x+2)=92x=10,x⩾3,x⩾−2∅∅−2x=8,x<3,x<−2x=5x=−4
Commented by hardmath last updated on 24/May/24
thank you so much
thankyousomuch
Answered by A5T last updated on 24/May/24
9=∣x−3∣+∣x+2∣≥∣2x−1∣ ⇒−9≤2x−1≤9⇒−4≤x≤5 Equality occurs at the boundary points ⇒x=−4 or 5
9=∣x−3∣+∣x+2∣⩾∣2x−1∣⇒−9⩽2x−1⩽9⇒−4⩽x⩽5Equalityoccursattheboundarypoints⇒x=−4or5

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *