<

≤

>

≥

<

≤

>

≥

=(-∞,∞)

={∅}

={∅}

<

≤

>

≥

<

≤

>

≥

<

≤

>

≥

<

≤

>

≥

Zoom -

Zoom +

{

=\left\{∅  \right\} 

{

{

a \; x+b<c

a \; x+b≤c

a \; x+b>c

a \; x+b≥c

a' \; x+b'<c'

a' \; x+b'≤c'

a' \; x+b'>c'

a' \; x+b'≥c'

a'1 = 0.7 (slider from -10 to 10, step 1.07)
a' = If(a'1 < 0, floor(a'1), a'1 > 0, ceil(a'1))
a1 = 2.84 (slider from -10 to 10, step 1.07)
a = If(a1 < 0, floor(a1), a1 > 0, ceil(a1))
b = -2 (slider from -10 to 10, step 1)
c = 1 (slider from -10 to 10, step 1)
Inec_1: {(a * x) + b < c, (a * x) + b ≤ c, (a * x) + b > c, (a * x) + b ≥ c}
e: (c - b) / a
d = 3 (slider from 1 to 4, step 1)
i'_1 = Element(Inec_1, d)
i_1 = Simplify(i'_1)
b' = 0 (slider from -12 to 12, step 1)
c' = 2 (slider from -12 to 12, step 1)
Inec_2: {(a' * x) + b' < c', (a' * x) + b' ≤ c', (a' * x) + b' > c', (a' * x) + b' ≥ c'}
e': (c' - b') / a'
m = Min(e, e')
texto31: "=(-∞," + (LaTeX[m]) + "]"
texto32: "=(-∞," + (LaTeX[m]) + ")"
n = Max(e, e')
texto37: "=[" + (LaTeX[m]) + "," + (LaTeX[n]) + ")"
texto17: "=[" + (LaTeX[m]) + "," + (LaTeX[n]) + "]"
texto18: "=(" + (LaTeX[m]) + "," + (LaTeX[n]) + "]"
texto38: "=(" + (LaTeX[m]) + "," + (LaTeX[n]) + ")"
texto33: "=[" + n + ",∞)"
texto34: "=(" + (LaTeX[n]) + ",∞)"
d' = 2 (slider from 1 to 4, step 1)
i'_2 = Element(Inec_2, d')
i_2 = Simplify(i'_2)
j(x) = i_1(x) ∧ i_2(x)
p_1: j(m - 0.01)
p: j(m)
p_2: j(m + 0.01)
c10: p_1 ≟ false ∧ p ≟ false ∧ p_2 ≟ false ∧ m ≟ n ∧ a ≠ 0 ∧ a' ≠ 0
c3: p ≟ true ∧ p_1 ≟ true ∧ p_2 ≟ false ∧ a ≠ 0 ∧ a' ≠ 0
c4: p ≟ false ∧ p_1 ≟ true ∧ p_2 ≟ false
q_2: j(n + 0.01)
q: j(n)
c9: q ≟ true ∧ q_2 ≟ true ∧ p_1 ≟ false ∧ a ≠ 0 ∧ a' ≠ 0
q_1: j(n - 0.01)
c1: p_1 ≟ false ∧ p ≟ true ∧ p_2 ≟ true ∧ q_1 ≟ true ∧ q ≟ true ∧ q_2 ≟ false
c2: p_1 ≟ false ∧ p ≟ false ∧ p_2 ≟ true ∧ q_1 ≟ true ∧ q ≟ true ∧ q_2 ≟ false
c6: p_1 ≟ false ∧ p ≟ true ∧ p_2 ≟ true ∧ q_1 ≟ true ∧ q ≟ false ∧ q_2 ≟ false
c7: p_1 ≟ false ∧ p ≟ false ∧ p_2 ≟ true ∧ q_1 ≟ true ∧ q ≟ false ∧ q_2 ≟ false
c8: p_1 ≟ false ∧ p ≟ false ∧ p_2 ≟ false ∧ q_1 ≟ false ∧ q ≟ false ∧ q_2 ≟ false ∧ a ≠ 0 ∧ a' ≠ 0
c5: q_1 ≟ false ∧ q ≟ false ∧ q_2 ≟ true ∧ a ≠ 0 ∧ a' ≠ 0
g: i_1(e)
z_1 = -1.5 (slider from -2 to 1, step 0.1)
g': i_2(e')
g'_1: i_2(e' - 0.01)
texto22_1: "\left.  " + (LaTeX[i_1]) + " \atop  " + (LaTeX[i_2]) + "
\right\}"
texto1 = LaTeX(i_1, true, true)
texto2_1 = LaTeX(i_2, true, true)
g'_2: i_2(e' + 0.01)
g_1: i_1(e - 0.01)
g_2: i_1(e + 0.01)
r = Line((1, z_1), (-1, z_1))
s = Ray((e, z_1), (e - 1, z_1))
A: (e, z_1)
s' = Mirror(s, A)
A': A
te: (z_1 * e)
texto2 = If(g_1, If[g_2, "(-∞,∞)", If[g, "(-∞," + e + "]", "(-∞," + e + ")"]], If[g, "[" + e + ",∞)", If[g_2, "(" + e + ",∞)", "{∅}"]])
texto4 = If(g'_1, If[g'_2, "(-∞,∞)", If[g', "(-∞," + e' + "]", "(-∞," + e' + ")"]], If[g', "[" + e' + ",∞)", If[g'_2, "(" + e' + ",∞)", "{∅}"]])
texto7: "Solución Primera Inecuación=" + texto2 + ""
texto8: "Solución Segunda Inecuación=" + texto4 + ""
r' = Line((1, (-z_1)), (-1, (-z_1)))
t' = Ray((e', (-z_1)), (e' - 1, (-z_1)))
B: (e', (-z_1))
t = Mirror(t', B)
B': B
r'' = Line((1, 0), (-1, 0))
u = Ray((e, 0), (e + 1, 0))
C: (e, 0)
texto22: "=[" + e + ",∞)"
C': C
texto23: "=(" + e + ",∞)"
u' = Mirror(u, C)
texto24: "=(-∞," + e + "]"
texto25: "=(-∞," + e + ")"
v = Ray((e', 0), (e' + 1, 0))
D: (e', 0)
texto26: "=[" + e' + ",∞)"
D': D
texto27: "=(" + e' + ",∞)"
v' = Mirror(v, D)
texto28: "=(-∞," + e' + "]"
texto29: "=(-∞," + e' + ")"
w = Ray((m, 0), (m - 1, 0))
E: (m, 0)
E': E
F: (n, 0)
w' = Ray((n, 0), (n + 1, 0))
F': F
f = Segment((m, 0), (n, 0))
texto35: "=[" + m + "," + n + "]"
texto36: "=(" + m + "," + n + "]"
texto9: "Solución Sistema Inecuaciones= " + texto2 + "∩" + texto4 + "="
texto10: "a=" + a + ""
texto11: "a'=" + a' + ""
texto3: "Solución =" + (LaTeX[texto2]) + ""
texto12: "b=" + b + ""
texto13: "c=" + c + ""
texto14 = SurdText(e)
texto15: "" + i'_1 + ""
E1: (e, 3)
h = Vector(A', E1)
E'1 = Translate(A', h)
s'' = Translate(s', h)
s'_1 = Translate(s, h)
A'_1 = Translate(A, h)
texto16: "" + (LaTeX[i'_2]) + ""
texto5: "Solución=" + (LaTeX[texto4]) + ""
i = Segment(E, F')
k = Segment(E, F)
l = Segment(E', F)
a_1 = Segment(E', F')
z_2: 1
texto19: "b'=" + b' + ""
texto20: "c'=" + c' + ""
texto41: "" + (LaTeX[texto15]) + ""
texto42: "" + (LaTeX[texto16]) + ""
texto46 = If(c1, texto17, c2, texto18, c3, texto31, c4, texto32, c5, texto34, c6, texto37, c7, texto38, c8, texto39, c9, texto33, c10, texto39)
texto47: "=" + m + ""
c11: p_1 ≟ false ∧ p ≟ true ∧ p_2 ≟ false ∧ m ≟ n ∧ a ≠ 0 ∧ a' ≠ 0
texto48 = If(c1, texto17, c2, texto18, c3, texto31, c4, texto32, c5, texto34, c6, texto37, c7, texto38, c8, texto39, c9, texto33, c10, texto39, c11, texto47)
texto6: "Solución=" + (LaTeX[texto2]) + "∩" + (LaTeX[texto4]) + "" + (LaTeX[texto48]) + ""