Einfache Gleichungen und Ungleichungen II
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Gib die Lösungsmenge von x für die folgen Gleichungen und Ungleichungen in der Grundmenge R an. nprvmulticols abclist abc x x + abc x x - abc x + x - abc -x + x - abc x + . abc x - . abc - x abc x + . - abc .x + x abc .x + .x abc .x + abc -.x . abc .x - abc .x abc .x - .x - abc x + .x abc x + . le - abc +x ge -. abc x le -.x - abc .x - ge - abc x + - abc x x + abc - x -.x + abc -x abclist nprvmulticols
Solution:
Übersicht über die Intervalle: minipagec.textwidth * leftabright qtyxinR| a le x le b leftabright qtyxinR| a x b leftabright qtyxinR| a le x b leftabright qtyxinR| a x le b * minipage hfill minipagec.textwidth * left-inftybright qtyxinR| x le b left-inftybright qtyxinR| x b leftainftyright qtyxinR| a le x leftainftyright qtyxinR| a x * minipage abclist abc edtx x + uf -x x uf : x frac loesfrac ed abc edtx x - uf -x x - uf : x - loes-ed abc edtx + x - uf -x+ x loesed abc edt-x + x - uf +x+ x uf : frac x loesfrac ed abc edtx + . uf - x . uf : x . loes.ed abc edtx - . uf + x . uf: x . loes.ed abc edt - x uf - -x uf :- x -frac loesfrac ed abc edtx + . - uf -. x -. uf : x -. loes.ed abc edt.x + x uf -.x -.x uf:-. -. x ed abc edt.x + .x uf -.x .x uf:. x loesed abc edt.x + uf - . x uf:. x loesed abc edt-.x . uf:-. x -. loes-.ed abc edt.x - uf :. x - loes-ed abc edt.x uf :. x frac loesfraced abc edt.x - .x - uf -.x + - .x uf:. - x loes- ed abc edtx + .x uf -x -.x uf :-. -frac x loes-fraced abc edtx + . &le - uf -. x &le -. && L -infty-.ed abc edt+x &ge -. uf - x &ge -. && L -.infty ed abc edtx &le -.x - uf +.x .x &le - uf:. x &le - && L left-infty-righted abc edt.x - &ge - uf + .x &ge uf:. x &ge frac &&L leftfrac inftyright ed abc edtx + & - uf - x & - uf : x & -frac && L left-fracinftyrighted abc edtx & x + uf-x -x & uf - x & - &&L left-infty-right ed abc edt - x & -.x + uf + x - & .x uf:. & x &&L qty-infty ed abc edt-x & uf:- x & - && L qty-infty-ed abclist
Gib die Lösungsmenge von x für die folgen Gleichungen und Ungleichungen in der Grundmenge R an. nprvmulticols abclist abc x x + abc x x - abc x + x - abc -x + x - abc x + . abc x - . abc - x abc x + . - abc .x + x abc .x + .x abc .x + abc -.x . abc .x - abc .x abc .x - .x - abc x + .x abc x + . le - abc +x ge -. abc x le -.x - abc .x - ge - abc x + - abc x x + abc - x -.x + abc -x abclist nprvmulticols
Solution:
Übersicht über die Intervalle: minipagec.textwidth * leftabright qtyxinR| a le x le b leftabright qtyxinR| a x b leftabright qtyxinR| a le x b leftabright qtyxinR| a x le b * minipage hfill minipagec.textwidth * left-inftybright qtyxinR| x le b left-inftybright qtyxinR| x b leftainftyright qtyxinR| a le x leftainftyright qtyxinR| a x * minipage abclist abc edtx x + uf -x x uf : x frac loesfrac ed abc edtx x - uf -x x - uf : x - loes-ed abc edtx + x - uf -x+ x loesed abc edt-x + x - uf +x+ x uf : frac x loesfrac ed abc edtx + . uf - x . uf : x . loes.ed abc edtx - . uf + x . uf: x . loes.ed abc edt - x uf - -x uf :- x -frac loesfrac ed abc edtx + . - uf -. x -. uf : x -. loes.ed abc edt.x + x uf -.x -.x uf:-. -. x ed abc edt.x + .x uf -.x .x uf:. x loesed abc edt.x + uf - . x uf:. x loesed abc edt-.x . uf:-. x -. loes-.ed abc edt.x - uf :. x - loes-ed abc edt.x uf :. x frac loesfraced abc edt.x - .x - uf -.x + - .x uf:. - x loes- ed abc edtx + .x uf -x -.x uf :-. -frac x loes-fraced abc edtx + . &le - uf -. x &le -. && L -infty-.ed abc edt+x &ge -. uf - x &ge -. && L -.infty ed abc edtx &le -.x - uf +.x .x &le - uf:. x &le - && L left-infty-righted abc edt.x - &ge - uf + .x &ge uf:. x &ge frac &&L leftfrac inftyright ed abc edtx + & - uf - x & - uf : x & -frac && L left-fracinftyrighted abc edtx & x + uf-x -x & uf - x & - &&L left-infty-right ed abc edt - x & -.x + uf + x - & .x uf:. & x &&L qty-infty ed abc edt-x & uf:- x & - && L qty-infty-ed abclist