Page 92 - math 12

R ﻲﻓ ِﺕﺍﻮﻄﺨﻟﺍ ِﺓﺩﺪﻌﺘﻣ ِﺔﻳﺮﺒﺠﻟﺍ ِﺕﺎﻨﻳﺎﺒﺘﻤﻟﺍ ﻞﺣ ُ ﺱﺭﺪﻟﺍ
ّ

Solving Multi-step Algebraic Inequalities in R [4-5]

ﱠ
ﻢﻠَﻌَﺗ ﺱﺭﺪﻟﺍ ُﺓﺮﻜﻓ
ِ
ﺔﻴﺣﻭﺮﻤﻟﺍ ﻰﻟﺍ ﺩﻮﻌﺼﻟﺍ ﺩﻮﻨﺟ ﺔﻳﺮﺒﺠﻟﺍ ِﺕﺎﻨﻳﺎﺒﺘﻤﻟﺍ ﻞـﺣ
ﺔﻴﺣﻭﺮﻤﻟﺍ ﻰﻟﺍ ﺩﻮﻌﺼﻟﺍ ﺩﻮﻨﺟ 8 ﺩﺍﺭﺃ ﺍﺫﺇ
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ﻪﺗﺍﺪﻌﻣ ﻦﻣ 20kg ﻢﻬﻨﻣ ﺪﺣﺍﻭ ﻞﻛ ﻞﻤﺤﻳﻭ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺕﺍﻮﻄﺨﻟﺍ ﺓﺩﺪﻌﺘﻣ
ﻪﺗﺍﺪﻌﻣ ﻦﻣ ّ ُ
ّ
. ﺔﻴﺼﺨﺸﻟﺍ ﻰﻠﻋ ﻞـﺤﻟﺍ ﻞﻴﺜﻤﺗﻭ ّ ﺹﺍﻮﺨﻟﺍ
ِ
ََ
ﻥﺯﻮﻟﺍ ﺩﺎﺠﻳﻻ ﺎﻬﻠﺣﻭ ﺔــﻨﻳﺎﺒﺘﻣ ْ ﺐﺘﻛﺃ
ﻥﺯﻮﻟﺍ ﺩﺎﺠﻳﻻ ﺎﻬﻠﺣﻭ ﺔــﻨﻳﺎﺒﺘﻣ ْ ﺐﺘﻛﺃ . ِﺩﺍﺪﻋﻷﺍ ﻢﻴﻘﺘﺴﻣ
ﺕﺍﺩﺮﻔﻤﻟﺍ
ﻰﻠﻋ ﻱﺪﻨﺟ ﻞﻜﻟ ﻪﺑ ﺡﻮﻤﺴﻤﻟﺍ ﻲﻓﺎﺿﻷﺍ .ﺔﻳﺮﺒﺠﻟﺍ ﺔﻨﻳﺎﺒﺘﻤﻟﺍ
ﻰﻠﻋ ﻱﺪﻨﺟ ﻞﻜﻟ ﻪﺑ ﺡﻮﻤﺴﻤﻟﺍ ﻲﻓﺎﺿﻷﺍ
ُ
ُ
.880kg ﻰﻠﻋ ﺔﻴﻠﻜﻟﺍ ﻢﻬُﺘﻟﻮﻤﺣ ﺪﻳﺰﺗﻻ ﻥﺃ .ُﺮﻴﻐﺘﻤﻟﺍ
.
ﺪﺣﺃ ﻲﻓ ً
ﺕﺎﻨﻳﺎﺒﺘﻤﻟﺍ
ﻞﺣ [
ﺍﺮﻴﻐﺘﻣ ُ
. ﺎﻬﻴﻓﺮﻁ ِﺪﺣﺃ ﻲﻓ ًﺍﺮﻴﻐﺘﻣ ُﻦﻤﻀﺘﺗ ﻲﺘﻟﺍﻭ ِﺕﺍﻮﻄﺨﻟﺍ ِﺓﺩﺪﻌﺘﻣ ِﺔﻳﺮﺒﺠﻟﺍ ِﺕﺎﻨﻳﺎﺒﺘﻤﻟﺍ ﻞﺣ [4-5-1]
ﺕﺍﻮﻄﺨﻟﺍ ِ
. ﺎﻬﻴﻓﺮﻁ ِ
ﺓﺩﺪﻌﺘﻣ ِ
ﺔﻳﺮﺒﺠﻟﺍ ِ
ﻦﻤﻀﺘﺗ ﻲﺘﻟﺍﻭ ِ
ّ
ّ
Solving Multi-steps Algebraic Inequalities Which has variable in one side
ﻲﻓ ﺮﻴﻐﺘﻤﻟﺍ ﻰﻠﻋ ﻱﻮﺘﺤﻳ ﻱﺬﻟﺍ ﺪﺤﻟﺍ ﻝﺰﻌﻟ ﺹﺍﻮﺨﻟﺍ ﻞﻤﻌﺘﺳﺍ ،ﺎﻬﻴﻓﺮﻁ ﺪﺣﺍ ﻲﻓ ﺮﻴﻐﺘﻣ ﻰﻠﻋ ﻱﻮﺘﺤﺗ ِﺔﻨﻳﺎﺒﺘﻣ ﻞﺤﻟ
ّ
ِ
ٍ
َ
،ِﺔﻨﻳﺎﺒﺘﻤﻠﻟ ﻞﺤﻟﺍ ﺔﻋﻮﻤﺠﻣ ْﺪﺟﻭ ِﺔﻤﺴﻘﻟﺍ ﻭﺍ ِﺏﺮﻀﻟﺍ ِﺔﻴﺻﺎﺧ ﻝﺎﻤﻌﺘﺳﺎﺑ ًﺍﺪﺣﺍﻭ ﻪﻠﻣﺎﻌﻣ ﻞﻌﺟﺍ ﻢﺛ ،ِﺔﻨﻳﺎﺒﺘﻤﻟﺍ ﻑﺮﻁ
ﱢ
. ِﺔﻴﻘﻴﻘﺤﻟﺍ ِﺩﺍﺪﻋﻷﺍ ﻢﻴﻘﺘﺴﻣ ﻰﻠﻋ ﻞﺤﻟﺍ ِﺔﻋﻮﻤﺠﻣ ﻞﺜﻤﺗ ﻦﻜﻤﻳﻭ
ِ
ﱢ
ً
َ
ﻞﻜﻟ ﻰﻟﺍ ﺎﻬﺑ ﺡﻮﻤﺴﻤﻟﺍ ﺔﻴﻓﺎﺿﻻﺍ ﺕﺎﻣﺍﺮﻏﻮﻠﻴﻜﻟﺍ ِﺩﺪﻋ ﺩﺎﺠﻳﻻ ﺎﻬّﻠﺣﻭ ﺔﻟﺄﺴﻤﻟﺍ ﻞﺜﻤﺗ ﺔﻨﻳﺎﺒﺘﻣ ْ ﺐﺘﻛﺃ (1) ﻝﺎﺜﻣ
ُ
ﱢ
. ﻱﺪﻨﺟ
ﻱﺪﻨﺟ ﻞﻜﻟ ﻪﺑ ﺡﻮﻤﺴﻤﻟﺍ ﻲﻓﺎﺿﻻﺍ ﻥﺯﻮﻟﺍ ﻞﺜﻤﻳ w َﺮﻴﻐﺘﻤﻟﺍ ﻥﺃ ُ ﺽﺮﻔﻧ
ّ
8(w + 20) ≤ 880
8w + 160 ≤ 880 ﺔﻨﻳﺎﺒﺘﻤﻟﺍ ﻲﻓﺮﻁ ﻰﻟﺍ - 160 ﻒﺿﺍ
8w ≤ 720 8 ﻰﻠﻋ ﺔﻨﻳﺎﺒﺘﻴﻤﻟﺍ ﻲﻓﺮﻁ ﻢﺴﻗﺍ
w ≤ 90 ﺔﻴﺣﻭﺮﻤﻟﺍ ﻰﻟﺍ ﻲﻓﺎﺿﻷﺍ ﻥﺯﻮﻟﺍ ﻦﻣ 90kg ﻞﻤﺤﻳ ﻥﺃ َﻱﺪﻨﺟ ﻞﻛ ُﻊﻴﻄﺘﺴﻳ
ّ
: ِﺩﺍﺪﻋﻷﺍ ﻢﻴﻘﺘﺴﻣ ﻰﻠﻋ ﻪّﻠﺜﻣﻭ ﱢ ﺹﺍﻮﺨﻟﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ R ﻲﻓ ِﺔﻴﻟﺎﺘﻟﺍ ِﺕﺎﻨﻳﺎﺒﺘﻤﻟﺍ ﻞﺣ (2) ﻝﺎﺜﻣ
ّ
ِ
i) 3(y-2) ≤ 6- 27 ⇒ 3y- 6 ≤ 3 ⇒ 3y ≤ 9 ⇒ y ≤ 3 1 2 3 4 5
3
..........
1
1
4
1
1
4
ii) (x - )+ x > - 10 ⇒ x + x > - 10 + ⇒ x > -1
2 3 2 6 2 2 6 6
-3 -2 -1 0 1 2 ..........
: ِﺔﻴﻘﻴﻘﺤﻟﺍ ِﺩﺍﺪﻋﻷﺍ ﻰﻠﻋ ِﺕﺎﻨﻳﺎﺒﺘﻤﻟﺍ ﱢ ﺹﺍﻮﺧ ﻝﺎﻤﻌﺘﺳﺎﺑ R ﻲﻓ ِﺔﻴﻟﺎﺘﻟﺍ ِﺕﺎﻨﻳﺎﺒﺘﻤﻟﺍ ﻞﺣ (3) ﻝﺎﺜﻣ
ّ
i) 5(z - 3 ) ≥ 10 (2 - 3 ) ⇒ z - 3 ≥ 4 -2 3 ⇒ z ≥ 4 -2 3 + 3 ⇒ z ≥ 4- 3
4
4
1
1
ii) v + -27 - v < | -3 | ⇒ v - v - 3 < 3 ⇒ - v < 6 ⇒ v > -6
3
3 3 3 3
iii) 9 - −8 > 5(x -1) ⇒ 9 +2 > 5x -5 ⇒ 11 > 5 x -5 ⇒ 16 > 5 x ⇒ x < 16
3
5
7
iv) -4 7 14 ) < 0 ⇒ -4 × h + -4 × 14 < 0 ⇒ -2h -1< 0 ⇒ -2h <1⇒h > -1
( h +
7 2 8 7 2 7 8 2
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