Kopertina e librit Matematika 9

Zgjidhja e ushtrimit 3

Zgjidhja e ushtrimit 3 të mësimit 9D në librin Matematika 9 nga shtëpia botuese Botime Pegi me autorë Deborah Barton.


Pyetja

Zgjidhni inekuacionet e mëposhtme.

Zgjidhja

  1. x>21x>21x1<21x<2-x > 2 \rArr -1x > 2 \rArr \dfrac{\cancel{-1}x}{\cancel{-1}} < \dfrac{2}{-1} \rArr x < -2 (ndryshohet kahu i shenjës kur pjesëtojmë me minus)
  2. 552211x2211x5555 \leq 22 - 11x \rArr 22-11x \geq 55 \rArr 11x5522-11x \geq 55-22 \rArr 11x33-11x \geq 33 \rArr 11x113311\dfrac{\cancel{-11}x}{\cancel{-11}} \leq \dfrac{33}{-11} \rArr x3x \leq -3
  3. 8(5x7)9558(5x-7)-9 \leq 55 \rArr 40x5695540x-56-9 \leq 55 \rArr 40x655540x-65 \leq 55 \rArr 40x55+6540x \leq 55+65 \rArr 40x12040x \leq 120 \rArr 40x4012040\dfrac{\cancel{40}x}{\cancel{40}} \leq \dfrac{120}{40} \rArr x3x \leq 3
  4. 5(3x+7)+6>915(3x+7)+6 > 91 \rArr 15x+35+6>9115x+35+6>91 \rArr 15x+41>9115x+41 > 91 \rArr 15x>914115x > 91-41 \rArr 15x>5015x > 50 \rArr 15x15>5015\dfrac{\cancel{15}x}{\cancel{15}} > \dfrac{50}{15} \rArr x>103x > \dfrac{10}{3}