1. Д умоляю!!! Срочно нужно!. Created by nastyasherlok. algebra-ru

1.а) (1/8)*x > 2 ⇔ x >16 , иначе x∈(16 ; ∞). б) 3 -5x <30 ⇔ 3- 30 < 5x ⇔ x > - 27/5= - 5,4,иначе x∈(-5,4 ; ∞).г) 4(x+1) ≤ x -2 ⇔ 4x + 4 ≤ x -2 ⇔ 4x - x ≤ -2 - 4 ⇔ 3x ≤ -6 ⇔x ≤ -2 , иначе x ∈ (-∞ ; -2].д) -2 ≤ 3x+1 ≤ 3 ⇔ -2 - 1 ≤ 3x ≤ 3 -1 ⇔ -3 ≤ 3x ≤ 2 ⇔ - 1 ≤ x ≤ 2/3 , иначе x∈ [ -1 ;2/3 ] . 2.а) { 0,2x>2 ; -3x < -12 ⇔ { x >10 ; x >4 ⇔ x >10, иначе x∈(10 ; ∞) .б) {6,5x -2 <1,5x -1 ; 2 - 3x < x+6 .⇔{6,5x - 1,5x < 2 -1 ; 2 -6 < x+ 3x. ⇔{5x < 1 ; -4 < 4x. ⇔ {x < 1/5 ; - 1 < x. ⇔ -1 < x < 1/5 , иначе x ∈ (-1 ; 1/5) .3.{0,5x +2 >1 ; 3x -1,6 < 0,8.⇔{0,5x >1 -2 ; 3x < 0,8 +1,6.⇔{ x > -2 ; x < 0,8. , иначе x ∈ (-2 ; 0,8).4.-4 < 10 -2x ≤ 4 ⇔ - 4 ≤ 2x -10 < 4 ⇔ - 4+10 ≤ 2x < 4 +10 ⇔ 3 ≤ x <7, иначе x ∈ [3 ; 7).liris22liris22-1 <= x <= 2/3Подробности во вложении. 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1. Д умоляю!!! Срочно нужно!...

nastyasherlok @nastyasherlok

July 2022 1 13 Report

1. Д умоляю!!! Срочно нужно!

Answers & Comments

liris22 1.
а)  (1/8)*x > 2 ⇔ x >16 , иначе  x∈(16 ; ∞).
б) 3 -5x <30 ⇔ 3- 30 < 5x ⇔ x > - 27/5= - 5,4,иначе  x∈(-5,4 ; ∞).
г) 4(x+1) ≤ x -2 ⇔ 4x + 4  ≤ x -2 ⇔ 4x - x ≤ -2 - 4 ⇔ 3x ≤ -6 ⇔x ≤ -2 ,
иначе x ∈ (-∞ ; -2].
д) -2 ≤ 3x+1 ≤ 3 ⇔ -2 - 1 ≤ 3x ≤ 3 -1 ⇔ -3 ≤ 3x  ≤ 2 ⇔ - 1 ≤ x  ≤ 2/3 , иначе  x∈ [ -1 ;2/3 ] .
2.
а) { 0,2x>2 ; -3x < -12 ⇔ { x >10 ; x >4 ⇔ x >10, иначе  x∈(10 ; ∞) .
б) {6,5x -2 <1,5x -1 ; 2 - 3x < x+6 .⇔{6,5x - 1,5x < 2 -1 ; 2 -6 < x+ 3x. ⇔
{5x < 1 ; -4 < 4x.  ⇔ {x < 1/5 ; - 1 < x. ⇔ -1 < x < 1/5 , иначе  x ∈ (-1 ; 1/5) .
3.
{0,5x +2 >1 ; 3x -1,6 < 0,8.⇔{0,5x >1 -2 ; 3x < 0,8 +1,6.⇔{ x > -2 ; x < 0,8.  , иначе  x ∈ (-2 ; 0,8).
4.
-4 < 10 -2x ≤ 4 ⇔ - 4  ≤ 2x -10 < 4 ⇔ - 4+10  ≤ 2x < 4 +10 ⇔ 3 ≤ x <7, иначе  x ∈ [3 ; 7).