02 emgega material de estudio semana 2

7𝑥 + 9 = −12 𝑥 = −3 𝑥2 + 4 𝑥 + 3 = 0 𝑥1 = −3

𝑥2 = −1

7𝑥 + 9 ≤ −12 𝑥 ≤ −3

𝑎, 𝑏

𝑥

(𝒂, 𝒃) = {𝒙 | 𝒂 < 𝒙 < 𝒃}

(𝑎, ∞) = {𝑥 | 𝑎 < 𝑥}

[𝒂, 𝒃] = {𝒙 | 𝒂 ≤ 𝒙 ≤ 𝒃}

(−∞, 𝑏) = {𝑥 | 𝑥 < 𝑏}

(𝒂, 𝒃] = {𝒙 | 𝒂 < 𝒙 ≤ 𝒃}

[𝑎, ∞) = {𝑥 | 𝑎 ≤ 𝑥}

[𝒂, 𝒃) = {𝒙 | 𝒂 ≤ 𝒙 < 𝒃}

(−∞, 𝑏] = {𝑥 | 𝑥 ≤ 𝑏}

7𝑥 + 9 ≤ −12 (−∞, 3]

𝑎≤𝑏 𝑎≤𝑏

𝑐>0

𝑎𝑐 ≤ 𝑏𝑐

𝑐

𝑎≤𝑏 𝑐<0 𝑎+𝑐 ≤ 𝑏+𝑐

7𝑥 + 9 ≤ −12

7𝑥 ≤ −21

𝑥≤−

21 = −3 7

(−∞, 3]

𝑎𝑐 ≥ 𝑏𝑐

𝑥 2 + 2𝑥 − 3 ≤ 0 𝑥 = −3 𝑥 = 1 𝑥 2 + 2𝑥 − 3 = (𝑥 + 3)(𝑥 − 1) ≤ 0

(𝑥 + 3)

(𝑥 − 1)

(𝑥 + 3)(𝑥 − 1) ≤ 0

(𝑥 + 3) ≤ 0

(𝑥 − 1) ≥ 0

(𝑥 + 3) ≥ 0

(𝑥 − 1) ≤ 0.

𝑥 ≤ −3

𝑥≥1

𝑥 ≥ −3

𝑥 ≤ 1. 𝑥 ∈ (−∞, −3] ∩ [1, ∞) 𝑥 ∈ [−3, ∞) ∩ (−∞, 1] 𝑥 ∈ ∅ ∪ [−3,1]

𝑥 ∈ [−3,1]

ЁЭСж = ЁЭСе 2 + 2ЁЭСе тИТ 3 ЁЭСе1 = тИТ3 [тИТ3,1]

ЁЭСе2 = 1