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𝐸𝑠 𝑢𝑛 𝑒𝑛𝑢𝑛𝑐𝑖𝑎𝑑𝑜 𝑒𝑛 𝑒𝑙 𝑞𝑢𝑒 𝑑𝑜𝑠
𝑒𝑥𝑝𝑟𝑒𝑠𝑖𝑜𝑛𝑒𝑠 𝑑𝑒𝑛𝑜𝑡𝑎𝑛 𝑒𝑙 𝒎𝒊𝒔𝒎𝒐 𝒗𝒂𝒍𝒐𝒓
𝒏𝒖𝒎é𝒓𝒊𝒄𝒐.
𝐷𝑜𝑠 𝑜𝑏𝑗𝑒𝑡𝑜𝑠 𝑚𝑎𝑡𝑒𝑚á𝑡𝑖𝑐𝑜𝑠 𝑠𝑜𝑛
𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑎𝑑𝑜𝑠 𝑖𝑔𝑢𝑎𝑙𝑒𝑠 𝑠𝑖 𝑙𝑜𝑠
𝑜𝑏𝑗𝑒𝑡𝑜𝑠 𝑝𝑜𝑠𝑒𝑒𝑛 𝑒𝑙 𝑚𝑖𝑠𝑚𝑜 𝑣𝑎𝑙𝑜𝑟.
𝑆𝑖𝑚𝑏𝑜𝑙𝑜𝑔í𝑎: " = "
𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠:
5 + 3 = 9 − 1
10 + 3 = 15 − 1
5 + 3 = 9 − 1
𝑃𝑟𝑖𝑚𝑒𝑟
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝑆𝑒𝑔𝑢𝑛𝑑𝑜
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝑉𝑒𝑟𝑖𝑓𝑖𝑐𝑎𝑟 𝑠𝑖 𝑠𝑜𝑛 𝑜 𝑛𝑜 𝑖𝑔𝑢𝑎𝑙𝑑𝑎𝑑𝑒𝑠:
5 + 4 = 9 − 2 5 + 3 = 9 − 1
𝑃𝑟𝑖𝑚𝑒𝑟
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝑆𝑒𝑔𝑢𝑛𝑑𝑜
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
25 + 5 = 3 ∗ 2
5 − 1 = 22
14 = 9 −1
5 ∗ 4 = 2 ∗ 12
60 ÷ 4 = 8 ∗ 5
35 ∗ 2 = 7 ∗ 10
10
= 1
𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠:
5 + 3 = 9 − 1
𝑃𝑟𝑖𝑚𝑒𝑟
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝑆𝑒𝑔𝑢𝑛𝑑𝑜
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠:
5 + 3 = 9 − 1
𝑃𝑟𝑖𝑚𝑒𝑟
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝑆𝑒𝑔𝑢𝑛𝑑𝑜
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝐸𝑠 𝑢𝑛𝑎 𝒊𝒈𝒖𝒂𝒍𝒅𝒂𝒅 𝒎𝒂𝒕𝒆𝒎á𝒕𝒊𝒄𝒂
𝑑𝑜𝑛𝑑𝑒 𝑠𝑒 𝑑𝑒𝑠𝑐𝑜𝑛𝑜𝑐𝑒𝑛 𝑐𝑖𝑒𝑟𝑡𝑜𝑠
𝑣𝑎𝑙𝑜𝑟𝑒𝑠 𝑙𝑙𝑎𝑚𝑎𝑑𝑜𝑠 𝑖𝑛𝑐ó𝑔𝑛𝑖𝑡𝑎𝑠.
𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠:
𝑥 + 3 = 15
5𝑥 + 3 = 𝑥 + 2
𝑃𝑟𝑖𝑚𝑒𝑟
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝑆𝑒𝑔𝑢𝑛𝑑𝑜
𝑚𝑖𝑒𝑚𝑏𝑟𝑜
𝐶𝑢𝑎𝑛𝑑𝑜 𝑠𝑒 ℎ𝑎𝑏𝑙𝑎 𝑑𝑒 𝒓𝒆𝒔𝒐𝒍𝒗𝒆𝒓
𝑢𝑛𝑎 𝑒𝑐𝑢𝑎𝑐𝑖ó𝑛 𝑠𝑒 𝑟𝑒𝑓𝑖𝑒𝑟𝑒 𝑎
𝑒𝑛𝑐𝑜𝑛𝑡𝑟𝑎𝑟 𝑐𝑖𝑒𝑟𝑡𝑜𝑠 𝑣𝑎𝑙𝑜𝑟𝑒𝑠
𝑞𝑢𝑒 𝑠𝑎𝑡𝑖𝑠𝑓𝑎𝑐𝑒𝑛 𝑑𝑖𝑐ℎ𝑎 𝑖𝑔𝑢𝑎𝑙𝑑𝑎𝑑
𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠:
𝐼𝑛𝑐ó𝑔𝑛𝑖𝑡𝑎𝑠:
𝐶𝑜𝑒𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑒𝑠 𝑖𝑛𝑐ó𝑔𝑛𝑖𝑡𝑎𝑠:
𝑃𝑟𝑖𝑚𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜:
𝑆𝑒𝑔𝑢𝑛𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜:
𝑇é𝑟𝑚𝑖𝑛𝑜𝑠 𝑑𝑒𝑙 1𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜:
𝑇é𝑟𝑚𝑖𝑛𝑜𝑠 𝑑𝑒𝑙 2𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜:
𝑇é𝑟𝑚𝑖𝑛𝑜𝑠 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑖𝑒𝑛𝑡𝑒𝑠:
𝐺𝑟𝑎𝑑𝑜 𝑒𝑐𝑢𝑎𝑐𝑖ó𝑛:
+ 3 = 15
𝑎 + 𝑐 = 𝑏 + 𝑐
𝑎 − 𝑐 = 𝑏 − 𝑐
𝑎 ∙ 𝑐 = 𝑏 ∙ 𝑐
𝑎
𝑐
=
𝑏
𝑐
𝑎 + 𝑐 = 𝑏 + 𝑐
𝑎 − 𝑐 = 𝑏 − 𝑐
𝑎 ∙ 𝑐 = 𝑏 ∙ 𝑐
𝑎
𝑐
=
𝑏
𝑐
𝑥 + 3 = 25
2𝑥 − 1 = 11 2𝑥 = 11 + 𝑥
22 + 3 = 25
2(11) = 11 + (11)
𝑚 + 8 = −2𝑚
2𝑧 + 101 = 𝑧
2𝑥 + 2 = 0

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1. igualdades copia

  • 1. 𝐸𝑠 𝑢𝑛 𝑒𝑛𝑢𝑛𝑐𝑖𝑎𝑑𝑜 𝑒𝑛 𝑒𝑙 𝑞𝑢𝑒 𝑑𝑜𝑠 𝑒𝑥𝑝𝑟𝑒𝑠𝑖𝑜𝑛𝑒𝑠 𝑑𝑒𝑛𝑜𝑡𝑎𝑛 𝑒𝑙 𝒎𝒊𝒔𝒎𝒐 𝒗𝒂𝒍𝒐𝒓 𝒏𝒖𝒎é𝒓𝒊𝒄𝒐. 𝐷𝑜𝑠 𝑜𝑏𝑗𝑒𝑡𝑜𝑠 𝑚𝑎𝑡𝑒𝑚á𝑡𝑖𝑐𝑜𝑠 𝑠𝑜𝑛 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑎𝑑𝑜𝑠 𝑖𝑔𝑢𝑎𝑙𝑒𝑠 𝑠𝑖 𝑙𝑜𝑠 𝑜𝑏𝑗𝑒𝑡𝑜𝑠 𝑝𝑜𝑠𝑒𝑒𝑛 𝑒𝑙 𝑚𝑖𝑠𝑚𝑜 𝑣𝑎𝑙𝑜𝑟. 𝑆𝑖𝑚𝑏𝑜𝑙𝑜𝑔í𝑎: " = " 𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠: 5 + 3 = 9 − 1 10 + 3 = 15 − 1 5 + 3 = 9 − 1 𝑃𝑟𝑖𝑚𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜 𝑆𝑒𝑔𝑢𝑛𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜
  • 2. 𝑉𝑒𝑟𝑖𝑓𝑖𝑐𝑎𝑟 𝑠𝑖 𝑠𝑜𝑛 𝑜 𝑛𝑜 𝑖𝑔𝑢𝑎𝑙𝑑𝑎𝑑𝑒𝑠: 5 + 4 = 9 − 2 5 + 3 = 9 − 1 𝑃𝑟𝑖𝑚𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜 𝑆𝑒𝑔𝑢𝑛𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜 25 + 5 = 3 ∗ 2 5 − 1 = 22 14 = 9 −1 5 ∗ 4 = 2 ∗ 12 60 ÷ 4 = 8 ∗ 5 35 ∗ 2 = 7 ∗ 10 10 = 1
  • 3. 𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠: 5 + 3 = 9 − 1 𝑃𝑟𝑖𝑚𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜 𝑆𝑒𝑔𝑢𝑛𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜
  • 4. 𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠: 5 + 3 = 9 − 1 𝑃𝑟𝑖𝑚𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜 𝑆𝑒𝑔𝑢𝑛𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜
  • 5. 𝐸𝑠 𝑢𝑛𝑎 𝒊𝒈𝒖𝒂𝒍𝒅𝒂𝒅 𝒎𝒂𝒕𝒆𝒎á𝒕𝒊𝒄𝒂 𝑑𝑜𝑛𝑑𝑒 𝑠𝑒 𝑑𝑒𝑠𝑐𝑜𝑛𝑜𝑐𝑒𝑛 𝑐𝑖𝑒𝑟𝑡𝑜𝑠 𝑣𝑎𝑙𝑜𝑟𝑒𝑠 𝑙𝑙𝑎𝑚𝑎𝑑𝑜𝑠 𝑖𝑛𝑐ó𝑔𝑛𝑖𝑡𝑎𝑠. 𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠: 𝑥 + 3 = 15 5𝑥 + 3 = 𝑥 + 2 𝑃𝑟𝑖𝑚𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜 𝑆𝑒𝑔𝑢𝑛𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜 𝐶𝑢𝑎𝑛𝑑𝑜 𝑠𝑒 ℎ𝑎𝑏𝑙𝑎 𝑑𝑒 𝒓𝒆𝒔𝒐𝒍𝒗𝒆𝒓 𝑢𝑛𝑎 𝑒𝑐𝑢𝑎𝑐𝑖ó𝑛 𝑠𝑒 𝑟𝑒𝑓𝑖𝑒𝑟𝑒 𝑎 𝑒𝑛𝑐𝑜𝑛𝑡𝑟𝑎𝑟 𝑐𝑖𝑒𝑟𝑡𝑜𝑠 𝑣𝑎𝑙𝑜𝑟𝑒𝑠 𝑞𝑢𝑒 𝑠𝑎𝑡𝑖𝑠𝑓𝑎𝑐𝑒𝑛 𝑑𝑖𝑐ℎ𝑎 𝑖𝑔𝑢𝑎𝑙𝑑𝑎𝑑 𝐸𝑗𝑒𝑚𝑝𝑙𝑜𝑠: 𝐼𝑛𝑐ó𝑔𝑛𝑖𝑡𝑎𝑠: 𝐶𝑜𝑒𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑒𝑠 𝑖𝑛𝑐ó𝑔𝑛𝑖𝑡𝑎𝑠: 𝑃𝑟𝑖𝑚𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜: 𝑆𝑒𝑔𝑢𝑛𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜: 𝑇é𝑟𝑚𝑖𝑛𝑜𝑠 𝑑𝑒𝑙 1𝑒𝑟 𝑚𝑖𝑒𝑚𝑏𝑟𝑜: 𝑇é𝑟𝑚𝑖𝑛𝑜𝑠 𝑑𝑒𝑙 2𝑑𝑜 𝑚𝑖𝑒𝑚𝑏𝑟𝑜: 𝑇é𝑟𝑚𝑖𝑛𝑜𝑠 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑖𝑒𝑛𝑡𝑒𝑠: 𝐺𝑟𝑎𝑑𝑜 𝑒𝑐𝑢𝑎𝑐𝑖ó𝑛: + 3 = 15
  • 6. 𝑎 + 𝑐 = 𝑏 + 𝑐 𝑎 − 𝑐 = 𝑏 − 𝑐 𝑎 ∙ 𝑐 = 𝑏 ∙ 𝑐 𝑎 𝑐 = 𝑏 𝑐
  • 7. 𝑎 + 𝑐 = 𝑏 + 𝑐 𝑎 − 𝑐 = 𝑏 − 𝑐 𝑎 ∙ 𝑐 = 𝑏 ∙ 𝑐 𝑎 𝑐 = 𝑏 𝑐
  • 8. 𝑥 + 3 = 25 2𝑥 − 1 = 11 2𝑥 = 11 + 𝑥 22 + 3 = 25 2(11) = 11 + (11)
  • 9. 𝑚 + 8 = −2𝑚 2𝑧 + 101 = 𝑧 2𝑥 + 2 = 0