Ecuaciones Con Modulo
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En los siguientes ejemplos pueden observar cómo resolver algunas ecuaciones que involucran módulos x =2 a) −2 x x =2 − d) 3 3 x=2
−2
–x= 2
↓
↓
x1 = 2
x2 = – 2
x
2
x
b)
x −5
=2
+ (x – 5) = 2 x=2+5
– (x – 5) = 2 x=–2+5
↓ x1 = 7
↓ x2 = 3 x2 = 4
c)
=
x x
x1 = 2
3
2
x
=6 − x
2
x
+ x
3
=6
=6
x
:3
=6
x x
=2
x1 = 2
x2 = – 2
(3 + x)2 – 4 = 0 (3 + x)2 = 4
e) 4
=2
3 +x
x2 = – 2
3
x
=2 −
3
x
=2 −
3
3 +x
=
4
=2
(3 + x) = 2
– (3 + x) = 2
x=2–3
x=–2–3
x1= – 1
x2= – 5
−2
–x= 2
↓
↓
x1 = 2
x2 = – 2
x
2
x
b)
x −5
=2
+ (x – 5) = 2 x=2+5
– (x – 5) = 2 x=–2+5
↓ x1 = 7
↓ x2 = 3 x2 = 4
c)
=
x x
x1 = 2
3
2
x
=6 − x
2
x
+ x
3
=6
=6
x
:3
=6
x x
=2
x1 = 2
x2 = – 2
(3 + x)2 – 4 = 0 (3 + x)2 = 4
e) 4
=2
3 +x
x2 = – 2
3
x
=2 −
3
x
=2 −
3
3 +x
=
4
=2
(3 + x) = 2
– (3 + x) = 2
x=2–3
x=–2–3
x1= – 1
x2= – 5
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