Kopertina e librit Matematika 10 - 11: Pjesa I

Zgjidhja e ushtrimit 2

Zgjidhja e ushtrimit 2 të mësimit 10.4A në librin Matematika 10 - 11: Pjesa I nga shtëpia botuese Botime Pegi me autorë Steve Fearnley, June Haighton, Steve Lomax, Peter Mullarkey, James Nicholson dhe Matt Nixon.

Pyetja

Zgjidhni inekuacionet lineare të mëposhtme.

  1. 2x>122x>12
  2. 2x+1<172x+1<17
  3. 3x−2<193x-2<19
  4. 5x−2≤285x-2 \leq 28
  5. 3(x−2)<363(x-2)<36
  6. 5(x−2)≤205(x-2)\leq 20
  7. 27≤9(x−2)27 \leq 9(x-2)
  8. −5<5(1+3x)-5<5(1+3x)
  9. 10>2x>210>2x>2
  10. 1<2x+1<171<2x+1<17
  11. 7≤3x−2<197 \leq 3x-2<19
  12. 3<5x−2≤283<5x-2 \leq 28
  13. −2≤5x+3≤23-2 \leq 5x+3 \leq 23
  14. −5<8x+3<19-5 < 8x+3 < 19
  15. −20<3x−5<19-20 < 3x-5 < 19
  16. −5<10+3x<−2-5 < 10+3x < -2

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Zgjidhja

  1. 2x2>122⇒x>6\dfrac{2x}{2} > \dfrac{12}{2} \rArr x>6
  2. 2x<17−1⇒2x2<162⇒x<82x<17-1 \rArr \dfrac{2x}{2} < \dfrac{16}{2} \rArr x<8
  3. 3x<19+2⇒3x3<213⇒x<73x<19+2 \rArr \dfrac{3x}{3} < \dfrac{21}{3} \rArr x<7
  4. 5x≤28+2⇒5x5≤305⇒x≤65x \leq 28+2 \rArr \dfrac{5x}{5} \leq \dfrac{30}{5} \rArr x \leq 6
  5. 3x−6<36⇒3x<36+6⇒3x3<423⇒x<143x-6<36 \rArr 3x<36+6 \rArr \dfrac{3x}{3} < \dfrac{42}{3} \rArr x<14
  6. 5x−10≤20⇒5x≤20+10⇒5x5≤305⇒x≤65x-10 \leq 20 \rArr 5x \leq 20+10 \rArr \dfrac{5x}{5} \leq \dfrac{30}{5} \rArr x \leq 6
  7. 27≤9x−18⇒27+18≤9x⇒459≤9x9⇒5≤x⇒x≥527 \leq 9x-18 \rArr 27+18 \leq 9x \rArr \dfrac{45}{9} \leq \dfrac{9x}{9} \rArr 5 \leq x \rArr x \geq 5
  8. −5<5+15x⇒−5−5<15x⇒−1015<15x15⇒−23<x⇒x>−23-5 < 5+15x \rArr -5-5<15x \rArr \dfrac{-10}{15} < \dfrac{15x}{15} \rArr -\dfrac{2}{3} < x \rArr x>-\dfrac{2}{3}
  9. 102>2x2>22⇒5>x>1\dfrac{10}{2} > \dfrac{2x}{2} > \dfrac{2}{2} \rArr 5>x>1
  10. 1−1<2x<17−1⇒0<2x<16⇒02<2x2<162⇒0<x<81-1<2x<17-1 \rArr 0<2x<16 \rArr \dfrac{0}{2} < \dfrac{2x}{2} < \dfrac{16}{2} \rArr 0<x<8
  11. 7+2≤3x<19+2⇒9≤3x<21⇒93≤3x3<213⇒3≤x<77+2 \leq 3x < 19+2 \rArr 9 \leq 3x < 21 \rArr \dfrac{9}{3} \leq \dfrac{3x}{3} < \dfrac{21}{3} \rArr 3 \leq x < 7
  12. 3+2<5x≤28+2⇒5<5x≤30⇒55<5x5≤305⇒1<x≤63+2<5x \leq 28+2 \rArr 5 < 5x \leq 30 \rArr \dfrac{5}{5} < \dfrac{5x}{5} \leq \dfrac{30}{5} \rArr 1<x \leq 6
  13. −2−3≤5x≤23−3⇒−5≤5x≤20⇒−55≤5x5≤205⇒−1≤x≤4-2-3 \leq 5x \leq 23-3 \rArr -5 \leq 5x \leq 20 \rArr \dfrac{-5}{5} \leq \dfrac{5x}{5} \leq \dfrac{20}{5} \rArr -1 \leq x \leq 4
  14. −5−3<8x<19−3⇒−8<8x>16⇒−88<8x8<168⇒−1<x<2-5-3 < 8x < 19-3 \rArr -8 < 8x > 16 \rArr \dfrac{-8}{8} < \dfrac{8x}{8} < \dfrac{16}{8} \rArr -1<x<2
  15. −20+5<3x<19+5⇒−15<3x<24⇒−153<3x3<243⇒−5<x<8-20+5 < 3x < 19+5 \rArr -15 < 3x < 24 \rArr \dfrac{-15}{3} < \dfrac{3x}{3} < \dfrac{24}{3} \rArr -5<x<8
  16. −5−10<3x<−2−10⇒−15<3x<−12⇒−153<3x3<−123⇒−5<x<−4-5-10 < 3x < -2-10 \rArr -15 <3x<-12 \rArr \dfrac{-15}{3} < \dfrac{3x}{3} < \dfrac{-12}{3} \rArr -5<x<-4