Ob-kauj ruam algebra yog qhov nrawm thiab yooj yim-vim nws tsuas yog siv ob kauj ruam. Txhawm rau daws qhov ob-kauj ruam algebraic equation, txhua yam koj yuav tsum ua yog cais qhov sib txawv uas siv ntxiv, rho tawm, sib npaug, lossis faib. Yog tias koj xav paub yuav daws li cas ob-kauj ruam algebraic equations hauv ntau txoj kev, tsuas yog ua raws cov theem no.
Kauj ruam
Txoj Kev 1 ntawm 3: Daws Teeb Meem nrog Ib Qhov Txawv
Kauj Ruam 1. Sau qhov teeb meem
Thawj kauj ruam los daws qhov sib npaug algebraic ob kauj ruam yog sau qhov teeb meem yog li koj tuaj yeem xav txog cov lus teb. Piv txwv tias koj xav daws qhov teeb meem no: -4x + 7 = 15.
Kauj Ruam 2. Txiav txim siab yog tias koj xav siv qhov sib ntxiv lossis rho tawm cais qhov sib txawv
Cov kauj ruam tom ntej yog xam seb yuav ua li cas thiaj tau -4x ntawm ib sab thiab qhov tsis tu ncua (tus lej tag nrho) ntawm lwm qhov. Txhawm rau ua qhov no, koj yuav tsum ua Kev Hloov Ntxiv, nrhiav qhov sib txawv ntawm +7, uas yog -7. Rho tawm 7 los ntawm ob sab ntawm qhov sib npaug kom +7, uas nyob rau ib sab ib yam li qhov sib txawv, ploj mus. Tsuas yog sau -7 hauv qab tus lej 7 ntawm ib sab thiab qis dua 15 ntawm lwm qhov kom cov zauv tseem nyob sib npaug.
Nco ntsoov Txoj Cai Zoo ntawm Algebra. Koj yuav tsum ua tib yam ntawm ob sab kom sib npaug qhov sib npaug. Tias yog vim li cas 15 kuj tseem raug txo los ntawm 7. Peb tsuas xav rho 7 ib zaug ntawm txhua sab, yog li -4x tsis tas yuav raug rho tawm ntawm 7
Kauj Ruam 3. Ntxiv lossis rho tawm qhov tsis sib xws ntawm ob sab ntawm kab zauv
Qhov no yuav cais qhov sib txawv. Rho tawm 7 los ntawm +7 ntawm sab laug ntawm kab zauv tshem tawm qhov tsis tu ncua ntawm sab laug ntawm kab zauv. Rho tawm 7 los ntawm +15 ntawm sab xis ntawm qhov kev ua zauv yuav muab tus lej rau koj 8. Yog li, qhov sib npaug tshiab yog -4x = 8.
- -4x + 7 = 15 =
- 4x -x = 8
Kauj Ruam 4. Tshem tawm qhov sib txawv coefficients los ntawm kev faib lossis sib npaug
Coefficient yog tus lej uas txuas rau qhov sib txawv. Hauv qhov piv txwv no, coefficient yog -4. Txhawm rau tshem -4 los ntawm -4x, koj yuav tsum faib ob sab ntawm qhov sib npaug los -4. Hauv qhov teeb meem no, x tau sib npaug los ntawm -4, yog li rov qab ua haujlwm no yog faib thiab koj yuav tsum faib ob tog.
Ib zaug ntxiv, koj yuav tsum ua tib yam ntawm ob sab. Tias yog vim li cas koj pom -4 ob zaug
Kauj Ruam 5. Nrhiav tus nqi ntawm qhov sib txawv
Txhawm rau ua qhov no, faib sab laug ntawm kab zauv, -4x, los -4, ua rau x. Faib sab xis ntawm kab zauv, 8, los -4, ua rau -2. Yog li, x = -2. Koj twb tau ua tiav ob kauj ruam - rho tawm thiab faib - los daws qhov kev ua zauv no.
Txoj Kev 2 ntawm 3: Daws Teeb Meem nrog Ib Qhov Txawv ntawm Txhua Sab
Kauj Ruam 1. Sau qhov teeb meem
Qhov teeb meem koj yuav ua haujlwm yog: -2x - 3 = 4x - 15. Ua ntej koj mus txuas ntxiv, xyuas kom tseeb tias ob qhov sib txawv sib npaug. Hauv qhov no, -2x thiab 4x muaj qhov sib txawv sib txawv, uas yog x, yog li koj tuaj yeem txav mus rau qib tom ntej.
Kauj Ruam 2. Tsiv qhov tas mus li mus rau sab xis ntawm kab zauv
Txhawm rau ua qhov no, koj yuav tsum ntxiv lossis rho tawm kom tshem qhov tas mus li los ntawm sab laug ntawm kab zauv. Qhov tsis tu ncua yog -3, yog li koj yuav tsum pom nws qhov sib txawv, uas yog +3, thiab ntxiv qhov tsis tu ncua no rau ob sab ntawm qhov sib npaug.
- Ntxiv +3 rau sab laug ntawm kab zauv, -2x -3, yuav ua rau (-2x -3) + 3 lossis -2x ntawm sab laug.
- Ntxiv +3 rau sab xis ntawm qhov sib npaug, 4x -15, muab (4x -15) +3 lossis 4x -12.
- Yog li, (-2x - 3) +3 = (4x - 15) +3 = -2x = 4x - 12
- Qhov sib npaug tshiab dhau los -2x = 4x -12
Kauj Ruam 3. Tsiv qhov sib txawv mus rau sab laug ntawm kab zauv
Txhawm rau ua qhov no, koj tsuas yog xav nrhiav qhov sib txawv ntawm 4x, uas yog -4x thiab rho tawm -4x los ntawm ob sab ntawm qhov sib npaug. Ntawm sab laug, -2x -4x = -6x, thiab ntawm sab xis, (4x -12) -4x = -12, yog li qhov sib npaug tshiab dhau los -6x = -12
2x - 4x = (4x - 12) - 4x = -6x = -12
Kauj Ruam 4. Nrhiav tus nqi ntawm qhov sib txawv
Tam sim no koj tau yooj yim qhov sib npaug rau -6x = -12, txhua yam koj yuav tsum tau ua yog faib ob sab ntawm qhov sib npaug los ntawm -6 kom cais qhov sib txawv x, uas tam sim no sib npaug -6. Ntawm sab laug ntawm kab zauv, -6x -6 = x, thiab ntawm sab xis ntawm qhov sib npaug, -12 -6 = 2. Yog li, x = 2.
- -6x -6 = -12 -6
- x = 2 os
Txoj Kev 3 ntawm 3: Lwm Txoj Hauv Kev Txhim Kho Ob-Kauj Ruam
Kauj Ruam 1. Daws qhov ob-kauj ruam sib npaug thaum khaws qhov sib txawv ntawm sab xis
Koj tuaj yeem daws qhov sib npaug ob kauj ruam thaum khaws cov kev hloov pauv ntawm sab xis. Tsuav koj cais nws, koj yuav tau txais qhov txiaj ntsig zoo ib yam. Piv txwv, 11 = 3 - 7x. Txhawm rau daws qhov no, koj thawj kauj ruam yog txhawm rau sib txuas qhov sib faib los ntawm kev rho tawm 3 los ntawm ob sab ntawm qhov sib npaug. Tom qab ntawd, koj yuav tsum faib ob sab ntawm qhov sib npaug ntawm -7 kom tau txais tus nqi x. Nov yog koj ua nws li cas:
- 11 = 3 - 7x = np
- 11 - 3 = 3 - 3 - 7x =
- 8 = - 7x = np
- 8/-7 = -7/7x
- -8/7 = x lossis -1.14 = x
Kauj Ruam 2. Daws qhov ob-theem kev ua zauv los ntawm kev sib npaug hauv cov kauj ruam kawg es tsis txhob faib
Lub hauv paus ntsiab lus ntawm kev daws qhov sib npaug zoo li qhov no ib txwm zoo ib yam: siv cov lej los sib txuas ua ntu zus, cais cov lej sib txawv, thiab tom qab ntawd cais cov lej sib txawv yam tsis muaj qhov sib txuam. Piv txwv tias koj xav daws qhov sib npaug x/5 + 7 = -3. Thawj kauj ruam koj yuav tsum ua yog rho 7 ntawm ob sab, ntxiv -3, thiab tom qab ntawd muab ob tog sib npaug 5 kom pom tus nqi x. Nov yog koj ua nws li cas:
- x/5 + 7 = -3 =
- (x/5 + 7) - 7 = -3 - 7 =
- x/5 = -10
- x/5 * 5 = -10 * 5
- x = -50
Lub tswv yim
- Thaum sib npaug lossis faib ob tus lej nrog cov cim sib txawv (piv txwv li, ib qho zoo thiab lwm qhov tsis zoo), qhov tshwm sim ib txwm tsis zoo. Yog tias ob qho cim sib npaug, ces cov lus teb yog tus lej zoo.
- Yog tias tsis muaj tus lej nyob hauv ntej ntawm x, xav tias nws yog 1x.
- Qhov tsis tas yuav tsum muaj nyob ntawm txhua sab. Yog tias tsis muaj tus lej ua raws x, xav tias nws yog x+0.
