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Ufumbuzi - Mishumaa ya jumla ama thamani halisi

Fomu halisi:

x = - 6, \frac{6}{5}

x=-6 , \frac{6}{5}

Fomu ya namba mchanganyiko:

x = - 6, 1 \frac{1}{5}

x=-6 , 1\frac{1}{5}

Fomu ya desimali:

x = - 6, 1.2

x=-6 , 1.2

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
$\frac{1}{3} | x - 3 | = \frac{1}{2} | x |$
pasipo na alama za thamani kamili:

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

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:

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

2. Suluhisha mlingano huo mbili kwa x

24 ziada steps

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

Zidisha sehemu:

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

Vunja kugawanywa:

$\frac{x}{3} + \frac{- 3}{3} = \frac{1}{2} x$

Pata kigezo kikuu cha kugawanya ya numerator na denominator:

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

Tenga na ghairi kigezo kikuu:

$\frac{x}{3} - 1 = \frac{1}{2} x$

Toa kutoka pande zote mbili:

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

Kusanya istilahi kama hizi:

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

Kukusanya vigezo:

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

Pata msingi wa kawaida mdogo:

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

Zidisha misingi:

$(\frac{(1 \cdot 2)}{6} + \frac{(- 1 \cdot 3)}{6}) x - 1 = (\frac{1}{2} \cdot x) - \frac{1}{2} x$

Zidisha namba za juu:

$(\frac{2}{6} + \frac{- 3}{6}) x - 1 = (\frac{1}{2} \cdot x) - \frac{1}{2} x$

Unganisha sehemu:

$\frac{(2 - 3)}{6} \cdot x - 1 = (\frac{1}{2} \cdot x) - \frac{1}{2} x$

Unganisha namba za juu:

$\frac{- 1}{6} \cdot x - 1 = (\frac{1}{2} \cdot x) - \frac{1}{2} x$

Unganisha sehemu:

$\frac{- 1}{6} \cdot x - 1 = \frac{(1 - 1)}{2} x$

Unganisha namba za juu:

$\frac{- 1}{6} \cdot x - 1 = \frac{0}{2} x$

Punguza kigezo kisicho na maana:

$\frac{- 1}{6} x - 1 = 0 x$

Rahisisha hesabu:

$\frac{- 1}{6} x - 1 = 0$

Jumlisha kwa pande zote mbili:

$(\frac{- 1}{6} x - 1) + 1 = 0 + 1$

Ondoa kuongeza sifuri:

$\frac{- 1}{6} x = 0 + 1$

Ondoa kuongeza sifuri:

$\frac{- 1}{6} x = 1$

Zidisha pande zote mbili kwa kugawanya kwa :

$(\frac{- 1}{6} x) \cdot \frac{6}{- 1} = 1 \cdot \frac{6}{- 1}$

Kusanya istilahi kama hizi:

$(\frac{- 1}{6} \cdot - 6) x = 1 \cdot \frac{6}{- 1}$

Zidisha vigezo:

$\frac{(- 1 \cdot - 6)}{6} x = 1 \cdot \frac{6}{- 1}$

Rahisisha hesabu:

$1 x = 1 \cdot \frac{6}{- 1}$

$x = 1 \cdot \frac{6}{- 1}$

Rahisisha hesabu:

$x = - 6$

26 ziada steps

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

Zidisha sehemu:

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

Vunja kugawanywa:

$\frac{x}{3} + \frac{- 3}{3} = \frac{1}{2} \cdot - x$

Pata kigezo kikuu cha kugawanya ya numerator na denominator:

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

Tenga na ghairi kigezo kikuu:

$\frac{x}{3} - 1 = \frac{1}{2} \cdot - x$

Kusanya istilahi kama hizi:

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

Zidisha vigezo:

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

Rahisisha hesabu:

$\frac{x}{3} - 1 = \frac{- 1}{2} x$

Jumlisha kwa pande zote mbili:

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

Kusanya istilahi kama hizi:

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

Kukusanya vigezo:

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

Pata msingi wa kawaida mdogo:

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

Zidisha misingi:

$(\frac{(1 \cdot 2)}{6} + \frac{(1 \cdot 3)}{6}) x - 1 = (\frac{- 1}{2} \cdot x) + \frac{1}{2} x$

Zidisha namba za juu:

$(\frac{2}{6} + \frac{3}{6}) x - 1 = (\frac{- 1}{2} \cdot x) + \frac{1}{2} x$

Unganisha sehemu:

$\frac{(2 + 3)}{6} \cdot x - 1 = (\frac{- 1}{2} \cdot x) + \frac{1}{2} x$

Unganisha namba za juu:

$\frac{5}{6} \cdot x - 1 = (\frac{- 1}{2} \cdot x) + \frac{1}{2} x$

Unganisha sehemu:

$\frac{5}{6} \cdot x - 1 = \frac{(- 1 + 1)}{2} x$

Unganisha namba za juu:

$\frac{5}{6} \cdot x - 1 = \frac{0}{2} x$

Punguza kigezo kisicho na maana:

$\frac{5}{6} x - 1 = 0 x$

Rahisisha hesabu:

$\frac{5}{6} x - 1 = 0$

Jumlisha kwa pande zote mbili:

$(\frac{5}{6} x - 1) + 1 = 0 + 1$

Ondoa kuongeza sifuri:

$\frac{5}{6} x = 0 + 1$

Ondoa kuongeza sifuri:

$\frac{5}{6} x = 1$

Zidisha pande zote mbili kwa kugawanya kwa :

$(\frac{5}{6} x) \cdot \frac{6}{5} = 1 \cdot \frac{6}{5}$

Kusanya istilahi kama hizi:

$(\frac{5}{6} \cdot \frac{6}{5}) x = 1 \cdot \frac{6}{5}$

Zidisha vigezo:

$\frac{(5 \cdot 6)}{(6 \cdot 5)} x = 1 \cdot \frac{6}{5}$

Rahisisha kugawanywa:

$x = 1 \cdot \frac{6}{5}$

Ondoa kuzidisha na moja:

$x = \frac{6}{5}$

3. Orodhesha suluhisho

$x = - 6, \frac{6}{5}$
(2 suluhisho(s))

4. Chora grafu

Kila mstari unawakilisha kazi ya upande mmoja wa equation:
$y = \frac{1}{3} | x - 3 |$
$y = \frac{1}{2} | x |$
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