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Be-calm-then-solve-x-2-7x-8-x-3-2-




Question Number 178612 by Acem last updated on 19/Oct/22
Be calm then solve ∣((x^2 +7x−8)/(x+3))∣≥ 2
Becalmthensolvex2+7x8x+3∣⩾2
Answered by cortano1 last updated on 19/Oct/22
 x≠−3   ∣x^2 +7x−8∣≥∣2x+6∣   (x^2 +7x−8+2x+6)(x^2 +7x−8−2x−6)≥0   (x^2 +9x−2)(x^2 +5x−14)≥0    [(x+(9/2))^2 −((89)/4)−](x+7)(x−2)≥0   (x+((9+(√(89)))/2))(x+(((9−(√(89)))/2)))(x+7)(x−2)≥0
x3x2+7x8∣⩾∣2x+6(x2+7x8+2x+6)(x2+7x82x6)0(x2+9x2)(x2+5x14)0[(x+92)2894](x+7)(x2)0(x+9+892)(x+(9892))(x+7)(x2)0
Commented by Acem last updated on 19/Oct/22
 Good sir! try to find the required x values    Tip: ∣P ∣≥ d ; d≥ 0 ⇒     Either P ≥ d     Or     P ≤ −d
Goodsir!trytofindtherequiredxvaluesTip:P∣⩾d;d0EitherPdOrPd
Commented by cortano1 last updated on 19/Oct/22
i don′t try it
idonttryit
Commented by Acem last updated on 19/Oct/22
Ok friend, you can check it below
Okfriend,youcancheckitbelow
Answered by Acem last updated on 19/Oct/22
  Either ((x^2 +7x−8)/(x+3))≥ 2 ∣_A    Or    ((x^2 +7x−8)/(x+3))≤ −2 ∣_B     A: (((x−2)(x+1))/(x+3))≥ 0        x       −∞           −7          −3            2           +∞  (x−2)(x+1)                +     0      −            −     0     +      x+3                 −             −     0     +            +     Frac.                −    0      +      ∥     −    0     +     Either x∈ [−7, −3[ ∪ [2, +∞[    B:  (((x+(9/2))^2 −((89)/4))/(x+3))≤ 0    x= ((−9− (√(89)))/2) ≅ −9.21  or x= ((−9+ (√(89)))/2) ≅ 0.21          x       −∞             x_1           −3            x_2            +∞  (x−2)(x+1)                +     0      −            −     0     +      x+3                 −             −     0     +            +     Frac.                −    0      +      ∥     −    0     +     Or x∈ ]−∞, ((−9− (√(89)))/2) ] ∪ ]−3, ((−9+ (√(89)))/2) ]
Eitherx2+7x8x+32AOrx2+7x8x+32BA:(x2)(x+1)x+30x732+(x2)(x+1)+00+x+30++Frac.0+0+Eitherx[7,3[[2,+[B:(x+92)2894x+30x=98929.21orx=9+8920.21xx13x2+(x2)(x+1)+00+x+30++Frac.0+0+Orx],9892]]3,9+892]

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