This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya, nitasuluhisha maswali haya hatua kwa hatua. 1. Rahisisha: 3x + 5x - 7 Hatua 1: Unganisha vigezo vinavyofanana (3x na 5x). 3x + 5x - 7 = (3+5)x - 7 Hatua 2: Fanya hesabu. 8x - 7 Jibu sahihi ni A. 2. Tatua kwa x: 5x - 3 = 17 Hatua 1: Ongeza 3 pande zote mbili za mlinganyo. 5x - 3 + 3 = 17 + 3 5x = 20 Hatua 2: Gawanya pande zote mbili kwa 5. (5x)/(5) = (20)/(5) x = 4 Jibu sahihi ni B. 3. LCM ya 15 na 25 ni ipi? Hatua 1: Tafuta vigawo vikuu vya 15 na 25. 15 = 3 × 5 25 = 5 × 5 = 5^2 Hatua 2: Tafuta LCM kwa kuchukua vigawo vikuu vyote na nguvu zao za juu zaidi. LCM(15, 25) = 3^1 × 5^2 LCM(15, 25) = 3 × 25 LCM(15, 25) = 75 Jibu sahihi ni C. 4. Rahisisha: 2(x + 3) + 4(x - 1) Hatua 1: Panua mabano. 2(x + 3) = 2x + 6 4(x - 1) = 4x - 4 Hatua 2: Unganisha maneno yaliyopanuliwa. 2x + 6 + 4x - 4 Hatua 3: Unganisha vigezo vinavyofanana na nambari zisizobadilika. (2x + 4x) + (6 - 4) 6x + 2 Jibu sahihi ni C. 5. Uwiano wa wavulana kwa wasichana darasani ni 4:5. Ikiwa kuna wavulana 80, kuna wasichana wangapi? Hatua 1: Weka uwiano kama sehemu. WavulanaWasichana = (4)/(5) Hatua 2: Tumia idadi ya wavulana (80) kupata idadi ya wasichana. Acha G iwe idadi ya wasichana. (80)/(G) = (4)/(5) Hatua 3: Tatua kwa G kwa kuzidisha msalaba. 4 × G = 80 × 5 4G = 400 Hatua 4: Gawanya pande zote mbili kwa 4. G = (400)/(4) G = 100 Jibu sahihi ni A. Majibu ya mwisho: 1. A) 8x - 7 2. B) x = 4 3. C) 75 4. C) 6x + 2 5. A) 100 Tuma swali linalofuata 📸