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Ufumbuzi - Mishumaa ya jumla ama thamani halisi

Fomu halisi:

x = \frac{44}{3}, - \frac{56}{13}

x=\frac{44}{3} , -\frac{56}{13}

Fomu ya namba mchanganyiko:

x = 14 \frac{2}{3}, - 4 \frac{4}{13}

x=14\frac{2}{3} , -4\frac{4}{13}

Fomu ya desimali:

x = 14.667, - 4.308

x=14.667 , -4.308

Tazama hatua

Maelezo kwa hatua

1. Andika mlingano bila alama za thamani kamili

Tumia sheria zifuatazo:
$| x | = | y |$ → $x = \pm y$ na $| x | = | y |$ → $\pm x = y$
andika chaguzi zote nne za usawa
$| \frac{4}{5} x + \frac{3}{5} | = | \frac{1}{2} x + 5 |$
pasipo na alama za thamani kamili:

$\| x \| = \| y \|$	$\| \frac{4}{5} x + \frac{3}{5} \| = \| \frac{1}{2} x + 5 \|$
$x = + y$	$(\frac{4}{5} x + \frac{3}{5}) = (\frac{1}{2} x + 5)$
$x = - y$	$(\frac{4}{5} x + \frac{3}{5}) = - (\frac{1}{2} x + 5)$
$+ x = y$	$(\frac{4}{5} x + \frac{3}{5}) = (\frac{1}{2} x + 5)$
$- x = y$	$- (\frac{4}{5} x + \frac{3}{5}) = (\frac{1}{2} x + 5)$

Mara baada ya kusawazisha, mlingano $x = + y$ na $+ x = y$ unakuwa sawa na mlingano $x = - y$ na $- x = y$ unakuwa sawa, kwa hivyo tunapata mlingano 2 tu:

$\| x \| = \| y \|$	$\| \frac{4}{5} x + \frac{3}{5} \| = \| \frac{1}{2} x + 5 \|$
$x = + y$ , $+ x = y$	$(\frac{4}{5} x + \frac{3}{5}) = (\frac{1}{2} x + 5)$
$x = - y$ , $- x = y$	$(\frac{4}{5} x + \frac{3}{5}) = - (\frac{1}{2} x + 5)$

2. Suluhisha mlingano huo mbili kwa x

26 ziada steps

$(\frac{4}{5} \cdot x + \frac{3}{5}) = (\frac{1}{2} x + 5)$

Toa kutoka pande zote mbili:

$(\frac{4}{5} x + \frac{3}{5}) - \frac{1}{2} \cdot x = (\frac{1}{2} x + 5) - \frac{1}{2} x$

Kusanya istilahi kama hizi:

$(\frac{4}{5} \cdot x + \frac{- 1}{2} \cdot x) + \frac{3}{5} = (\frac{1}{2} \cdot x + 5) - \frac{1}{2} x$

Kukusanya vigezo:

$(\frac{4}{5} + \frac{- 1}{2}) x + \frac{3}{5} = (\frac{1}{2} \cdot x + 5) - \frac{1}{2} x$

Pata msingi wa kawaida mdogo:

$(\frac{(4 \cdot 2)}{(5 \cdot 2)} + \frac{(- 1 \cdot 5)}{(2 \cdot 5)}) x + \frac{3}{5} = (\frac{1}{2} \cdot x + 5) - \frac{1}{2} x$

Zidisha misingi:

$(\frac{(4 \cdot 2)}{10} + \frac{(- 1 \cdot 5)}{10}) x + \frac{3}{5} = (\frac{1}{2} \cdot x + 5) - \frac{1}{2} x$

Zidisha namba za juu:

$(\frac{8}{10} + \frac{- 5}{10}) x + \frac{3}{5} = (\frac{1}{2} \cdot x + 5) - \frac{1}{2} x$

Unganisha sehemu:

$\frac{(8 - 5)}{10} \cdot x + \frac{3}{5} = (\frac{1}{2} \cdot x + 5) - \frac{1}{2} x$

Unganisha namba za juu:

$\frac{3}{10} \cdot x + \frac{3}{5} = (\frac{1}{2} \cdot x + 5) - \frac{1}{2} x$

Kusanya istilahi kama hizi:

$\frac{3}{10} \cdot x + \frac{3}{5} = (\frac{1}{2} \cdot x + \frac{- 1}{2} x) + 5$

Unganisha sehemu:

$\frac{3}{10} \cdot x + \frac{3}{5} = \frac{(1 - 1)}{2} x + 5$

Unganisha namba za juu:

$\frac{3}{10} \cdot x + \frac{3}{5} = \frac{0}{2} x + 5$

Punguza kigezo kisicho na maana:

$\frac{3}{10} x + \frac{3}{5} = 0 x + 5$

Ondoa kuongeza sifuri:

$\frac{3}{10} x + \frac{3}{5} = 5$

Toa kutoka pande zote mbili:

$(\frac{3}{10} x + \frac{3}{5}) - \frac{3}{5} = 5 - \frac{3}{5}$

Unganisha sehemu:

$\frac{3}{10} x + \frac{(3 - 3)}{5} = 5 - \frac{3}{5}$

Unganisha namba za juu:

$\frac{3}{10} x + \frac{0}{5} = 5 - \frac{3}{5}$

Punguza kigezo kisicho na maana:

$\frac{3}{10} x + 0 = 5 - \frac{3}{5}$

Ondoa kuongeza sifuri:

$\frac{3}{10} x = 5 - \frac{3}{5}$

Geuza namba ya kawaida kuwa sehemu:

$\frac{3}{10} x = \frac{25}{5} + \frac{- 3}{5}$

Unganisha sehemu:

$\frac{3}{10} x = \frac{(25 - 3)}{5}$

Unganisha namba za juu:

$\frac{3}{10} x = \frac{22}{5}$

Zidisha pande zote mbili kwa kugawanya kwa :

$(\frac{3}{10} x) \cdot \frac{10}{3} = (\frac{22}{5}) \cdot \frac{10}{3}$

Kusanya istilahi kama hizi:

$(\frac{3}{10} \cdot \frac{10}{3}) x = (\frac{22}{5}) \cdot \frac{10}{3}$

Zidisha vigezo:

$\frac{(3 \cdot 10)}{(10 \cdot 3)} x = (\frac{22}{5}) \cdot \frac{10}{3}$

Rahisisha kugawanywa:

$x = (\frac{22}{5}) \cdot \frac{10}{3}$

Zidisha sehemu:

$x = \frac{(22 \cdot 10)}{(5 \cdot 3)}$

Rahisisha hesabu:

$x = \frac{44}{3}$

27 ziada steps

$(\frac{4}{5} x + \frac{3}{5}) = - (\frac{1}{2} x + 5)$

Panua mabano:

$(\frac{4}{5} \cdot x + \frac{3}{5}) = \frac{- 1}{2} x - 5$

Jumlisha kwa pande zote mbili:

$(\frac{4}{5} x + \frac{3}{5}) + \frac{1}{2} \cdot x = (\frac{- 1}{2} x - 5) + \frac{1}{2} x$

Kusanya istilahi kama hizi:

$(\frac{4}{5} \cdot x + \frac{1}{2} \cdot x) + \frac{3}{5} = (\frac{- 1}{2} \cdot x - 5) + \frac{1}{2} x$

Kukusanya vigezo:

$(\frac{4}{5} + \frac{1}{2}) x + \frac{3}{5} = (\frac{- 1}{2} \cdot x - 5) + \frac{1}{2} x$

Pata msingi wa kawaida mdogo:

$(\frac{(4 \cdot 2)}{(5 \cdot 2)} + \frac{(1 \cdot 5)}{(2 \cdot 5)}) x + \frac{3}{5} = (\frac{- 1}{2} \cdot x - 5) + \frac{1}{2} x$

Zidisha misingi:

$(\frac{(4 \cdot 2)}{10} + \frac{(1 \cdot 5)}{10}) x + \frac{3}{5} = (\frac{- 1}{2} \cdot x - 5) + \frac{1}{2} x$

Zidisha namba za juu:

$(\frac{8}{10} + \frac{5}{10}) x + \frac{3}{5} = (\frac{- 1}{2} \cdot x - 5) + \frac{1}{2} x$

Unganisha sehemu:

$\frac{(8 + 5)}{10} \cdot x + \frac{3}{5} = (\frac{- 1}{2} \cdot x - 5) + \frac{1}{2} x$

Unganisha namba za juu:

$\frac{13}{10} \cdot x + \frac{3}{5} = (\frac{- 1}{2} \cdot x - 5) + \frac{1}{2} x$

Kusanya istilahi kama hizi:

$\frac{13}{10} \cdot x + \frac{3}{5} = (\frac{- 1}{2} \cdot x + \frac{1}{2} x) - 5$

Unganisha sehemu:

$\frac{13}{10} \cdot x + \frac{3}{5} = \frac{(- 1 + 1)}{2} x - 5$

Unganisha namba za juu:

$\frac{13}{10} \cdot x + \frac{3}{5} = \frac{0}{2} x - 5$

Punguza kigezo kisicho na maana:

$\frac{13}{10} x + \frac{3}{5} = 0 x - 5$

Ondoa kuongeza sifuri:

$\frac{13}{10} x + \frac{3}{5} = - 5$

Toa kutoka pande zote mbili:

$(\frac{13}{10} x + \frac{3}{5}) - \frac{3}{5} = - 5 - \frac{3}{5}$

Unganisha sehemu:

$\frac{13}{10} x + \frac{(3 - 3)}{5} = - 5 - \frac{3}{5}$

Unganisha namba za juu:

$\frac{13}{10} x + \frac{0}{5} = - 5 - \frac{3}{5}$

Punguza kigezo kisicho na maana:

$\frac{13}{10} x + 0 = - 5 - \frac{3}{5}$

Ondoa kuongeza sifuri:

$\frac{13}{10} x = - 5 - \frac{3}{5}$

Geuza namba ya kawaida kuwa sehemu:

$\frac{13}{10} x = \frac{- 25}{5} + \frac{- 3}{5}$

Unganisha sehemu:

$\frac{13}{10} x = \frac{(- 25 - 3)}{5}$

Unganisha namba za juu:

$\frac{13}{10} x = \frac{- 28}{5}$

Zidisha pande zote mbili kwa kugawanya kwa :

$(\frac{13}{10} x) \cdot \frac{10}{13} = (\frac{- 28}{5}) \cdot \frac{10}{13}$

Kusanya istilahi kama hizi:

$(\frac{13}{10} \cdot \frac{10}{13}) x = (\frac{- 28}{5}) \cdot \frac{10}{13}$

Zidisha vigezo:

$\frac{(13 \cdot 10)}{(10 \cdot 13)} x = (\frac{- 28}{5}) \cdot \frac{10}{13}$

Rahisisha kugawanywa:

$x = (\frac{- 28}{5}) \cdot \frac{10}{13}$

Zidisha sehemu:

$x = \frac{(- 28 \cdot 10)}{(5 \cdot 13)}$

Rahisisha hesabu:

$x = \frac{- 56}{13}$

3. Orodhesha suluhisho

$x = \frac{44}{3}, - \frac{56}{13}$
(2 suluhisho(s))

4. Chora grafu

Kila mstari unawakilisha kazi ya upande mmoja wa equation:
$y = | \frac{4}{5} x + \frac{3}{5} |$
$y = | \frac{1}{2} x + 5 |$
Equation ni kweli ambapo mistari miwili inavuka.

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Kwa nini kujifunza hii

Tunakutana na thamani halisi karibu kila siku. Kwa mfano: Ikiwa utatembea maili 3 kwenda shuleni, je, unatembea pia minus 3 maili unaporudi nyumbani? Jibu ni hapana kwa sababu umbali hutumia thamani halisi. Thamani halisi ya umbali kati ya nyumbani na shuleni ni maili 3, huko au kurudi.
Kifupi, thamani halisi hutusaidia kukabiliana na dhana kama umbali, mipaka ya thamani zinazowezekana, na upotofu kutoka kwa thamani iliyowekwa.

Ufumbuzi - Mishumaa ya jumla ama thamani halisi

Maelezo kwa hatua

1. Andika mlingano bila alama za thamani kamili

2. Suluhisha mlingano huo mbili kwa x

3. Orodhesha suluhisho

4. Chora grafu

Kwa nini kujifunza hii

Vigezo na mada

Viungo vinavyohusiana

Ufumbuzi - Mishumaa ya jumla ama thamani halisi

Maelezo kwa hatua

1. Andika mlingano bila alama za thamani kamili

2. Suluhisha mlingano huo mbili kwa x

3. Orodhesha suluhisho

4. Chora grafu

Kwa nini kujifunza hii

Vigezo na mada

Viungo vinavyohusiana

Maswali ya hivi karibuni yaliyohusiana yalisuluhishwa