10.2: Kutatua na Kubadilisha kutofautiana, na Kuandika Majibu katika Uthibitishaji wa Muda
- Page ID
- 164789
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Ili kutatua na kutofautiana kwa grafu:
- Tatua usawa kwa kutumia Mali ya Usawa kutoka sehemu iliyopita.
- Grafu suluhisho lililowekwa kwenye mstari wa nambari.
- Andika suluhisho lililowekwa katika notation ya muda.
Tatua usawa, graph ufumbuzi uliowekwa kwenye mstari wa nambari na uonyeshe suluhisho lililowekwa katika maelezo ya muda:
- \(−1 ≤ 2x − 5 < 7\)
- \(x^2 + 7x + 10 < 0\)
- \(−6 < x − 2 < 4\)
Suluhisho
- \(\begin{array} &&−1 ≤ 2x − 5 < 7 &\text{Example problem} \\ &−1 + 5 ≤ 2x − 5 + 5 < 7 + 5 &\text{The goal is to isolate the variable \(x\), hivyo kuanza kwa kuongeza\(5\) mikoa yote mitatu katika usawa.}\\ &4 ≤ 2x <12 &\ maandishi {Kurahisisha.}\\ &\ dfrac {4} {2} ≤ 2x^2 <\ dfrac {4} {2} {2} &\ Nakala {Gawanya yote kwa\(2\) kutenganisha variable\(x\).}\\ &2 ≤ x <6 &\ Nakala {Jibu la mwisho lililoandikwa ukosefu wa uhaba/ufumbuzi kuweka fomu.}\\ & [2, 6) &\ Nakala {Jibu la mwisho lililoandikwa katika nukuu ya muda (angalia sehemu ya Nukuu ya Muda kwa maelezo zaidi)}\ mwisho {safu}\)
- \(\begin{array} &&x^2 + 7x + 10 < 0 &\text{Example problem} \\ &(x + 5)(x + 2) < 0 &\text{Factor the polynomial.} \\ &(x + 5)(x + 2) < 0 &\text{The product must be less than \(0\), ambayo ina maana kwamba kama\((x + 5) > 0\), basi\((x + 2) < 0\). Vile vile\((x + 5) < 0\), ikiwa, basi\((x + 2) > 0\).}\\ & (x + 5) > 0 (x + 2) < 0 &\ text {Find the intersection of each of these inequalities.}\\ &x > -5 x <-2 &\ maandishi {Pata makutano ya kila moja ya usawa huu.} \ mwisho {safu}\)


\(\begin{array} &&\;\;\;−5 < x < −2 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;&\text{Final answer written in inequality/solution set form.} \\ &\;\;\;(−5, −2) \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;&\text{Final answer written in interval notation (see section on Interval Notation for more details).} \end{array}\)
- \(\begin{array}&&−6 < x − 2 ≤ 4 &\text{Example problem} \\ &−6 + 2 < x − 2 + 2 ≤ 4 + 2 &\text{The goal is to isolate the variable \(x\), hivyo kuanza\(2\) kwa kuongeza mikoa yote mitatu katika usawa.}\\ &-4 <x ≤ 6 &\ maandishi {Jibu la mwisho lililoandikwa katika fomu ya kutosawa/ufumbuzi uliowekwa.}\\ & (-4, 6] &\ maandishi {Jibu la mwisho lililoandikwa katika nukuu ya muda (angalia sehemu ya Nukuu ya Muda kwa maelezo zaidi).} \ mwisho {safu}\)
Tatua kutofautiana, graph seti ya suluhisho kwenye mstari wa nambari na uonyeshe seti ya suluhisho katika nukuu ya muda:
- \(0 ≤ x + 1 ≤ 4\)
- \(0 < 2(x − 1) ≤ 4\)
- \(6 < 2(x − 1) < 12\)
- \(x^2 − 6x − 16 < 0\)
- \(2x^2 − x − 15 > 0\)