Page 80 - math 12

R ﻲﻓ ٍﺕﺍﻮﻄﺧ ِﺓﺪﻌﺑ ٍﺪﺣﺍﻭ ﺮﻴﻐﺘﻤﺑ ﻰﻟﻭﻻﺍ ِﺔﺟﺭﺪﻟﺍ ﻦﻣ ٍﺕﻻﺩﺎﻌﻣ ﻞﺣ ُ ﺱﺭﺪﻟﺍ
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Solving Multi-Step First Degree Equations with One Variable in R [4-2]

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ﻢﻠَﻌَﺗ ﺱﺭﺪﻟﺍ ُﺓﺮﻜﻓ
ِ
،ﺔﻤﻘﻓ
ﹾﺕﺩﺍﺯ
ﺕﺩﺍﺯ ،ﺔﻤﻘﻓ ِ ُ
ﹾﺕﺩﺍﺯ ،ﺔﻤﻘﻓ 600 ﻞﺣﺎﺴﻟﺍ ﻰﻠﻋ ﺔﺟﺭﺪﻟﺍ ﻦﻣ ٍﺔﻟﺩﺎﻌﻣ ﻞﺣ
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1
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ﺪﻌﺑﻭ ،ﺓﺩﻻﻮﻟﺍ ﺔﺠﻴﺘﻧ ﺎﻫﺩﺪﻋ ِﺓﺪﻌﺑ ٍﺪﺣﺍﻭ ﺮﻴﻐﺘﻤﺑ ﻰﻟﻭﻻﺍ
ﺪﻌﺑﻭ ،ﺓﺩﻻﻮﻟﺍ ﺔﺠﻴﺘﻧ ﺎﻫﺩﺪﻋ
6 .ٍﺕﺍﻮﻄﺧ
ﻥﺎﺘﻴﺤﻟﺍ
ﻥﺎﺘﻴﺤﻟﺍ ﻞﺒﻗ ﻦﻣ ﻡﻮﺠﻫ ﻰﻟﺍ ﺎﻬﺿﺮﻌﺗ ﺕﺍﺩﺮﻔﻤﻟﺍ
ﻡﻮﺠﻫ
ﻰﻟﺍ
ﺎﻬﺿﺮﻌﺗ

ﻞﺒﻗ
ﻦﻣ
ِ
ِ
.ﺔﻤﻘﻓ
.ﺔﻤﻘﻓ 550 ﻰﻟﺍ ﺎﻫﺩّﺪﻋ ﻞﻗ ،ﻕﺭﺰﻟﺍ .ﻊﻳﺯﻮﺘﻟﺍ ﺔﻴﺻﺎﺧ
ُ
ِ
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؟ ًﺓﺩﻮﻘﻔﻤﻟﺍ ِﺕﺎﻤﻘﻔﻟﺍ ُﺩﺪﻋﺎﻣ .ﻊﻴﻤﺠﺘﻟﺍ ﺔﻴﺻﺎﺧ
ِ
ﺎﻤﻬﻴﻠﻛ ﻭﺃ ﺎﻬﻴﻓﺮﻁ ﺪﺣﺃ ﻲﻓ ً ﺍﺮﻴﻐﺘﻣ ﻦﻤﻀﺘﺗ ﻲﺘﻟﺍ ِ ﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ [
ﺎﻤﻬﻴﻠﻛ ﻭﺃ ﺎﻬﻴﻓﺮﻁ ﺪﺣﺃ ﻲﻓ ًﺍﺮﻴﻐﺘﻣ ﻦﻤﻀﺘﺗ ﻲﺘﻟﺍ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ [4-2-1]
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Solving the Equations Which has variable in one side or both sides
ﻞﻌﺟﺍ ﻢﺛ ﺎﻬﻴﻓﺮﻁ ﺪﺣﺃ ﻲﻓ ﺮﻴﻐﺘﻤﻟﺍ ﻰﻠﻋ ﻱﻮﺘﺤﻳ ﻱﺬﻟﺍ ﺪﺤﻟﺍ ﻝﺰﻋﺍ ، ٍﺪﺣﺍﻭ ﺮﻴﻐﺘﻣ ﻰﻠﻋ ﻱﻮﺘﺤﺗ ﻲﺘﻟﺍ ِﺔﻟﺩﺎﻌﻤﻟﺍ ﻞﺤﻟ
ﱢ
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. ( ...... ،ﻊﻴﻤﺠﺘﻟﺍ، ﻊﻳﺯﻮﺘﻟﺍ) ِﺔﻴﻘﻴﻘﺤﻟﺍ ِﺩﺍﺪﻋﻻﺍ ﺹﺍﻮﺧ ﻝﺎﻤﻌﺘﺳﺎﺑ ًﺍﺪﺣﺍﻭ ﻪﻠﻣﺎﻌﻣ
n ﻮﻫ ﺓﺩﻮﻘﻔﻤﻟﺍ ﺕﺎﻤﻘﻔﻟﺍ َﺩﺪﻋ ّﻥﺃ ْ ﺽﺮﻓﺍ ، ﺓﺩﻮﻘﻔﻤﻟﺍ ﺕﺎﻤﻘﻔﻟﺍ ﺩﺪﻋ ﺩﺎﺠﻳﻹ (1) ﻝﺎﺜﻣ
1
ﻲﻫ ﺔﻟﺄﺴﻤﻟﺍ ﻞﺜﻤﺗ ﻲﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ
600 + × 600 - n = 550
6
600 + 100 - n = 550 1 × 600 ﺞﺗﺎﻧ ﺪﺟ
700 - n = 550 6
- n = 550 - 700 ﻑﺮﻁ ﻲﻓ ﺮﻴﻐﺘﻤﻟﺍ ﺪﺣ ﻝﺰﻋﺍ
- n = -150
(-1) ﻲﻓ ﺔﻟﺩﺎﻌﻤﻟﺍ ﻲﻓﺮﻁ ﺏﺮﺿﺍ
n = 150 . ﺔﻤﻘﻓ 150 ﻮﻫ ﺓﺩﻮﻘﻔﻤﻟﺍ ﺕﺎﻤﻘﻔﻟﺍ ﺩﺪﻋ ﺍﺬﻟ
ﻦﻣ(LS)ﺮﺴﻳﻷﺍ ﻑﺮﻄﻟﺎﺑ ﻞﺤﻟﺍ ﻦﻣ ﺎﻬﻴﻠﻋ ﺖﻠﺼﺣ ﻲﺘﻟﺍ (n=150)ﺮﻴﻐﺘﻤﻟﺍ ﺔﻤﻴﻗ ﻦﻋ ﺽ ّ ﻮﻋ :ُﻖّﻘﺤﺘﻟﺍ

: ﺔﻟﺩﺎﻌﻤﻟﺍ
1
600 + × 600 - n = 550
6
1
LS = 600 + × 600 - n = 600 + 100 - 150 = 550 = RS (ﻦﻤﻳﻷﺍ ﻑﺮﻄﻟﺍ)
6

: ِﺔﻴﻘﻴﻘﺤﻟﺍ ِﺩﺍﺪﻋﻻﺍ ّ ﺹﺍﻮﺧ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻴﻟﺎﺘﻟﺍ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ (2) ﻝﺎﺜﻣ
ّ
i) 2(z -8) +16 = |-36| ⇒ 2z-16 +16 = 36 ⇒ 2z = 36 ⇒ z = 36÷ 2 ⇒ z = 18

ii) 4(x -5 3 ) = 3x - 2 3 ⇒ 4x - 20 3 = 3x - 2 3

⇒ 4x - 3x = 20 3 - 2 3 ⇒ x = 18 3

1 2 3 2
iii) (3y + 10)-7 = (y - 15) ⇒ y + 2 -7 = y - 6
5
5
5
5
3 2 1
⇒ y - y = 5 - 6 ⇒ y = -1 ⇒ y = -5
5
5
5
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