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Ufumbuzi - Mishumaa ya jumla ama thamani halisi

Fomu halisi:

x = - \frac{216}{11}, - \frac{54}{13}

x=-\frac{216}{11} , -\frac{54}{13}

Fomu ya namba mchanganyiko:

x = - 19 \frac{7}{11}, - 4 \frac{2}{13}

x=-19\frac{7}{11} , -4\frac{2}{13}

Fomu ya desimali:

x = - 19.636, - 4.154

x=-19.636 , -4.154

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
$| \frac{4}{9} x + 5 | = | \frac{1}{27} x - 3 |$
pasipo na alama za thamani kamili:

$\| x \| = \| y \|$	$\| \frac{4}{9} x + 5 \| = \| \frac{1}{27} x - 3 \|$
$x = + y$	$(\frac{4}{9} x + 5) = (\frac{1}{27} x - 3)$
$x = - y$	$(\frac{4}{9} x + 5) = - (\frac{1}{27} x - 3)$
$+ x = y$	$(\frac{4}{9} x + 5) = (\frac{1}{27} x - 3)$
$- x = y$	$- (\frac{4}{9} x + 5) = (\frac{1}{27} x - 3)$

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:

$\| x \| = \| y \|$	$\| \frac{4}{9} x + 5 \| = \| \frac{1}{27} x - 3 \|$
$x = + y$ , $+ x = y$	$(\frac{4}{9} x + 5) = (\frac{1}{27} x - 3)$
$x = - y$ , $- x = y$	$(\frac{4}{9} x + 5) = - (\frac{1}{27} x - 3)$

2. Suluhisha mlingano huo mbili kwa x

21 ziada steps

$(\frac{4}{9} \cdot x + 5) = (\frac{1}{27} x - 3)$

Toa kutoka pande zote mbili:

$(\frac{4}{9} x + 5) - \frac{1}{27} \cdot x = (\frac{1}{27} x - 3) - \frac{1}{27} x$

Kusanya istilahi kama hizi:

$(\frac{4}{9} \cdot x + \frac{- 1}{27} \cdot x) + 5 = (\frac{1}{27} \cdot x - 3) - \frac{1}{27} x$

Kukusanya vigezo:

$(\frac{4}{9} + \frac{- 1}{27}) x + 5 = (\frac{1}{27} \cdot x - 3) - \frac{1}{27} x$

Pata msingi wa kawaida mdogo:

$(\frac{(4 \cdot 3)}{(9 \cdot 3)} + \frac{- 1}{27}) x + 5 = (\frac{1}{27} \cdot x - 3) - \frac{1}{27} x$

Zidisha misingi:

$(\frac{(4 \cdot 3)}{27} + \frac{- 1}{27}) x + 5 = (\frac{1}{27} \cdot x - 3) - \frac{1}{27} x$

Zidisha namba za juu:

$(\frac{12}{27} + \frac{- 1}{27}) x + 5 = (\frac{1}{27} \cdot x - 3) - \frac{1}{27} x$

Unganisha sehemu:

$\frac{(12 - 1)}{27} \cdot x + 5 = (\frac{1}{27} \cdot x - 3) - \frac{1}{27} x$

Unganisha namba za juu:

$\frac{11}{27} \cdot x + 5 = (\frac{1}{27} \cdot x - 3) - \frac{1}{27} x$

Kusanya istilahi kama hizi:

$\frac{11}{27} \cdot x + 5 = (\frac{1}{27} \cdot x + \frac{- 1}{27} x) - 3$

Unganisha sehemu:

$\frac{11}{27} \cdot x + 5 = \frac{(1 - 1)}{27} x - 3$

Unganisha namba za juu:

$\frac{11}{27} \cdot x + 5 = \frac{0}{27} x - 3$

Punguza kigezo kisicho na maana:

$\frac{11}{27} x + 5 = 0 x - 3$

Ondoa kuongeza sifuri:

$\frac{11}{27} x + 5 = - 3$

Toa kutoka pande zote mbili:

$(\frac{11}{27} x + 5) - 5 = - 3 - 5$

Ondoa kuongeza sifuri:

$\frac{11}{27} x = - 3 - 5$

Rahisisha hesabu:

$\frac{11}{27} x = - 8$

Zidisha pande zote mbili kwa kugawanya kwa :

$(\frac{11}{27} x) \cdot \frac{27}{11} = - 8 \cdot \frac{27}{11}$

Kusanya istilahi kama hizi:

$(\frac{11}{27} \cdot \frac{27}{11}) x = - 8 \cdot \frac{27}{11}$

Zidisha vigezo:

$\frac{(11 \cdot 27)}{(27 \cdot 11)} x = - 8 \cdot \frac{27}{11}$

Rahisisha kugawanywa:

$x = - 8 \cdot \frac{27}{11}$

Zidisha sehemu:

$x = \frac{(- 8 \cdot 27)}{11}$

Rahisisha hesabu:

$x = \frac{- 216}{11}$

22 ziada steps

$(\frac{4}{9} x + 5) = - (\frac{1}{27} x - 3)$

Panua mabano:

$(\frac{4}{9} \cdot x + 5) = \frac{- 1}{27} x + 3$

Jumlisha kwa pande zote mbili:

$(\frac{4}{9} x + 5) + \frac{1}{27} \cdot x = (\frac{- 1}{27} x + 3) + \frac{1}{27} x$

Kusanya istilahi kama hizi:

$(\frac{4}{9} \cdot x + \frac{1}{27} \cdot x) + 5 = (\frac{- 1}{27} \cdot x + 3) + \frac{1}{27} x$

Kukusanya vigezo:

$(\frac{4}{9} + \frac{1}{27}) x + 5 = (\frac{- 1}{27} \cdot x + 3) + \frac{1}{27} x$

Pata msingi wa kawaida mdogo:

$(\frac{(4 \cdot 3)}{(9 \cdot 3)} + \frac{1}{27}) x + 5 = (\frac{- 1}{27} \cdot x + 3) + \frac{1}{27} x$

Zidisha misingi:

$(\frac{(4 \cdot 3)}{27} + \frac{1}{27}) x + 5 = (\frac{- 1}{27} \cdot x + 3) + \frac{1}{27} x$

Zidisha namba za juu:

$(\frac{12}{27} + \frac{1}{27}) x + 5 = (\frac{- 1}{27} \cdot x + 3) + \frac{1}{27} x$

Unganisha sehemu:

$\frac{(12 + 1)}{27} \cdot x + 5 = (\frac{- 1}{27} \cdot x + 3) + \frac{1}{27} x$

Unganisha namba za juu:

$\frac{13}{27} \cdot x + 5 = (\frac{- 1}{27} \cdot x + 3) + \frac{1}{27} x$

Kusanya istilahi kama hizi:

$\frac{13}{27} \cdot x + 5 = (\frac{- 1}{27} \cdot x + \frac{1}{27} x) + 3$

Unganisha sehemu:

$\frac{13}{27} \cdot x + 5 = \frac{(- 1 + 1)}{27} x + 3$

Unganisha namba za juu:

$\frac{13}{27} \cdot x + 5 = \frac{0}{27} x + 3$

Punguza kigezo kisicho na maana:

$\frac{13}{27} x + 5 = 0 x + 3$

Ondoa kuongeza sifuri:

$\frac{13}{27} x + 5 = 3$

Toa kutoka pande zote mbili:

$(\frac{13}{27} x + 5) - 5 = 3 - 5$

Ondoa kuongeza sifuri:

$\frac{13}{27} x = 3 - 5$

Rahisisha hesabu:

$\frac{13}{27} x = - 2$

Zidisha pande zote mbili kwa kugawanya kwa :

$(\frac{13}{27} x) \cdot \frac{27}{13} = - 2 \cdot \frac{27}{13}$

Kusanya istilahi kama hizi:

$(\frac{13}{27} \cdot \frac{27}{13}) x = - 2 \cdot \frac{27}{13}$

Zidisha vigezo:

$\frac{(13 \cdot 27)}{(27 \cdot 13)} x = - 2 \cdot \frac{27}{13}$

Rahisisha kugawanywa:

$x = - 2 \cdot \frac{27}{13}$

Zidisha sehemu:

$x = \frac{(- 2 \cdot 27)}{13}$

Rahisisha hesabu:

$x = \frac{- 54}{13}$

3. Orodhesha suluhisho

$x = - \frac{216}{11}, - \frac{54}{13}$
(2 suluhisho(s))

4. Chora grafu

Kila mstari unawakilisha kazi ya upande mmoja wa equation:
$y = | \frac{4}{9} x + 5 |$
$y = | \frac{1}{27} x - 3 |$
Equation ni kweli ambapo mistari miwili inavuka.

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Kwa nini kujifunza hii

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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