\Leftrightarrow

El valor de x que cumple esa igualdad es:

(si el resultado es fracción, usa la barra /, por ejemplo, 2/3)

Wt45 = (-2.2, -0.8200000000000001)
a = Random(-5, 5)
c0 = Random(-4, 4)
β = 2.0943951023931953 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
b = Random(-4, 4)
c = If(c0 ≟ a, If[c0 > 0, c0 - 1, c0 + 1], c0)
d = Random(-5, 5)
sol: (d - b) / (a - c)
es = 1 (slider from -5 to 5, step 0.1)
b_1: es
ht: (2 * b_1)
a_1: (2 * es)
A = Point(Line[(5.58, 0), (5.58, 1)])
B: A + (a_1, b_1)
C: A + (a_1, (-b_1))
i = Line(B, C)
D: A - (a_1, b_1)
c_1: (6 * es)
I: D - (c_1, (2 * b_1))
H: D - (c_1, 0)
f = Segment(H, I)
T = (-3.1, -2.14)
L_2: T - (0, 0.82)
e = Line(T, T + (1, 0))
n = Line(L_2, e)
N_2 = Intersect(n, i)
M_2 = Intersect(n, f)
H_2 = Point(n)
q = CircleArc(H_2, Rotate[H_2 + (0, 0.5), (-β), H_2], Rotate[H_2 + (0, 0.5), β, H_2])
I_2 = Point(q)
α1 = Angle(I_2, H_2, H_2 + (0, 0.5))
nx1 = If(α1 > 180°, (-round((360° - α1) / (β / 9))), round(α1 / (β / 9)))
r = Vector(M_2, H_2)
O_2: N_2 + r
f_1 = CircleArc(O_2, Rotate[O_2 + (0, 0.5), (-β), O_2], Rotate[O_2 + (0, 0.5), β, O_2])
K_2 = Point(f_1)
α3 = Angle(K_2, O_2, O_2 + (0, 0.5))
nx3 = If(α3 > 180°, (-round((360° - α3) / (β / 9))), round(α3 / (β / 9)))
P_2 = Point(n)
e_1 = CircleArc(P_2, Rotate[P_2 + (0, 0.5), (-β), P_2], Rotate[P_2 + (0, 0.5), β, P_2])
J_2 = Point(e_1)
α2 = Angle(J_2, P_2, P_2 + (0, 0.5))
nx2 = If(α2 > 180°, (-round((360° - α2) / (β / 9))), round(α2 / (β / 9)))
pI: (nx1 * sol) + nx2
s = Vector(M_2, P_2)
Q_2: N_2 + s
g_1 = CircleArc(Q_2, Rotate[Q_2 + (0, 0.5), (-β), Q_2], Rotate[Q_2 + (0, 0.5), β, Q_2])
R_2 = Point(g_1)
α4 = Angle(R_2, Q_2, Q_2 + (0, 0.5))
nx4 = If(α4 > 180°, (-round((360° - α4) / (β / 9))), round(α4 / (β / 9)))
pD: (nx3 * sol) + nx4
hd = If(pD ≟ pI, b_1, If[pD > pI, (0.2 * b_1), (1.8 * b_1)])
hi: ht - hd
Wt44 = (-2.64, -0.2)
Wt43 = (-1.6600000000000001, -0.34)
Wt42 = (-2.08, 0.36)
Wt41 = (-0.76, 0.8200000000000001)
Wt40 = (-2.96, 0.6)
Wt39 = (-2.46, 1.1)
Wt38 = (-1.32, 0.38)
Wt37 = (-1.78, 1.08)
arriba = 0.7
abajo = 4
hp = 0.2
rb = 0.1
d_1: (0.4 * c_1)
J = Midpoint(H, D)
M: J - (rb, 0)
L: J + (rb, 0)
F: C + (c_1, 0)
K = Midpoint(C, F)
O: K - (rb, 0)
N: K + (rb, 0)
P: O + (0, hd)
Z: P - (d_1, 0)
A_1: Z + (0, hp)
W_1 = Midpoint(A_1, Z)
Q: N + (0, hd)
W: Q + (d_1, 0)
B_1: W + (0, hp)
Z_1 = Midpoint(B_1, W)
A_2 = Midpoint(W_1, Z_1)
R: M + (0, hi)
V: R - (d_1, 0)
C_1: V + (0, hp)
R_1 = Midpoint(C_1, V)
S: L + (0, hi)
U: S + (d_1, 0)
D_1: U + (0, hp)
S_1 = Midpoint(D_1, U)
T_1 = Midpoint(R_1, S_1)
m = Segment(R_1, T_1)
V_1 = Point(m)
z = Vector(R_1, V_1)
G_2: A_2 + z
U_1 = Point(m)
w = Vector(R_1, U_1)
F_2: A_2 + w
C_2: W_1 + z
B_2: W_1 + w
E_2: T_1 + z
D_2: T_1 + w
E: A + ((-a_1), b_1)
G: C + (c_1, (-((2 * b_1))))
polígono1: {Polygon[C_1, V, U, D_1]}
polígono2: {Polygon[S, L, M, R]}
polígono3: {Polygon[H, I, G, F]}
polígono4: {Polygon[D, E, B, C]}
polígono5: {Polygon[O, P, Q, N]}
polígono6: {Polygon[A_1, Z, W, B_1]}
F_1: A + (0, (3.8 * es))
G_1 = Rotate(F_1, 29.999999999999996°, A)
H_1 = Rotate(F_1, 329.99999999999994°, A)
Fiel = If(pD ≟ pI, F_1, If[pD > pI, H_1, G_1])
c1 = Circle(A, (0.4 * es))
g = Segment(A, Fiel)
I_1 = Intersect(c1, g, 1)
h = Segment(I_1, Fiel)
c2 = Circle(A, (3.8 * es))
E_1 = Point(e)
J_1 = Intersect(e, f)
u = Vector(J_1, E_1)
K_1 = Intersect(e, i)
L_1: K_1 + u
j = OrthogonalLine(A, e)
sI = If(nx2 ≟ 0, "", If[nx2 > 0, "+", "-"])
sD = If(nx4 ≟ 0, "", If[nx4 > 0, "+", "-"])
M_1 = Intersect(e, j)
k = OrthogonalLine(J, e)
l = OrthogonalLine(K, e)
N_1 = Intersect(e, k)
O_1 = Intersect(e, l)
P_1 = Point(e)
v = Vector(N_1, P_1)
Q_1: O_1 + v
texto6 = If(pI ≟ pD, "=", If[pI > pD, ">", "<"])
coef1 = If(a ≟ 1, "", "" + a)
coef2 = If(c ≟ 1, "", "" + c)
Ww1: U_1 + (0, arriba - 0.3)
Ww2: U_1 + (0, (2 * arriba) - 0.3)
Ww9: V_1 + (0, (4 * arriba) - 0.3)
Ww3: U_1 + (0, (3 * arriba) - 0.3)
Ww4: U_1 + (0, (4 * arriba) - 0.3)
Ww5: U_1 + (0, (5 * arriba) - 0.3)
Ww6: V_1 + (0, arriba - 0.3)
Ww7: V_1 + (0, (2 * arriba) - 0.3)
Wy1: D_2 + (0, arriba - 0.3)
Ww8: V_1 + (0, (3 * arriba) - 0.3)
Wy2: D_2 + (0, (2 * arriba) - 0.3)
Wy3: D_2 + (0, (3 * arriba) - 0.3)
Wy4: D_2 + (0, (4 * arriba) - 0.3)
Wy6: E_2 + (0, arriba - 0.3)
Wy5: D_2 + (0, (5 * arriba) - 0.3)
Wy7: E_2 + (0, (2 * arriba) - 0.3)
Wy8: E_2 + (0, (3 * arriba) - 0.3)
Wy9: E_2 + (0, (4 * arriba) - 0.3)
Wx1: F_2 + (0, arriba - 0.3)
Wz5: B_2 + (0, (5 * arriba) - 0.3)
Wz2: B_2 + (0, (2 * arriba) - 0.3)
Wz6: C_2 + (0, arriba - 0.3)
Wz3: B_2 + (0, (3 * arriba) - 0.3)
Wz7: C_2 + (0, (2 * arriba) - 0.3)
Wz8: C_2 + (0, (3 * arriba) - 0.3)
Wz9: C_2 + (0, (4 * arriba) - 0.3)
Wz1: B_2 + (0, arriba - 0.3)
Wz4: B_2 + (0, (4 * arriba) - 0.3)
Wx2: F_2 + (0, (2 * arriba) - 0.3)
Wx3: F_2 + (0, (3 * arriba) - 0.3)
Wx4: F_2 + (0, (4 * arriba) - 0.3)
Wx6: G_2 + (0, arriba - 0.3)
Wx5: F_2 + (0, (5 * arriba) - 0.3)
Wx7: G_2 + (0, (2 * arriba) - 0.3)
Wx8: G_2 + (0, (3 * arriba) - 0.3)
Wx9: G_2 + (0, (4 * arriba) - 0.3)
p = Circle(H_2, 0.5)
t = Circle(A, 0.37)
texto4: "" + (abs(nx2))
h_1 = Circle(P_2, J_2)
k_1 = Circle(O_2, K_2)
p_1 = Circle(Q_2, R_2)
i_1 = Segment(H_2, I_2)
j_1 = Segment(P_2, J_2)
l_1 = Segment(O_2, K_2)
m_1 = Segment(Q_2, R_2)
texto5: "" + (abs(nx4))
q_1 = Circle(H_2, 0.15)
r_1 = Circle(H_2, 0.15)
s_1 = Circle(P_2, 0.15)
t_1 = Circle(O_2, 0.15)
c_2 = Circle(Q_2, 0.15)
d_2 = Circle(P_2, 0.15)
e_2 = Circle(O_2, 0.15)
f_2 = Circle(Q_2, 0.15)
n_1 = Segment(D, H)
a_2 = Segment(E, D)
b_2 = Segment(E, B)
g_2 = Segment(B, C)
h_2 = Segment(C, F)
i_2 = Segment(F, G)
j_2 = Segment(G, I)
texto8: "" + (If[nx1 ≟ 1 ∨ nx1 ≟ 0, "", If[nx1 ≟ -1, "-", "" + nx1]]) + (If[nx1 ≟ 0, "", "\;x\;"]) + (If[(nx2 ≠ 0) ∧ ((nx1 ≠ 0) ∨ (nx2  <  0)), If[nx2 > 0, "+", "-"], ""]) + (If[nx2 ≠ 0, "" + "\;" + (abs(nx2)), ""]) + (If[nx1 ≟ 0 ∧ nx2 ≟ 0, "0", ""]) + "\;=\;" + (If[nx3 ≟ 1 ∨ nx3 ≟ 0, "", If[nx3 ≟ -1, "-", "" + nx3]]) + (If[nx3 ≟ 0, "", "\;x\;"]) + (If[(nx4 ≠ 0) ∧ ((nx3 ≠ 0) ∨ (nx4  <  0)), If[nx4 > 0, "+", "-"], ""]) + (If[nx4 ≠ 0, "" + "\;" + (abs(nx4)), ""]) + (If[nx3 ≟ 0 ∧ nx4 ≟ 0, "0", ""])
B1 = NaN
D1 = If(B1 ≟ sol, "MUY BIEN, ese es el valor correcto", "?")
k_2 = Circle(H_2, 0.5)
p_2 = Circle(P_2, J_2)
q_2 = Circle(O_2, K_2)
r_2 = Circle(Q_2, R_2)
Ws42: Wt42 + (0, hi)
Ws43: Wt43 + (0, hi)
s42 = Segment(R_1, Ws42)
Ws45: Wt45 + (0, hi)
s43 = Segment(R_1, Ws43)
Ws37: Wt37 + (0, hi)
s45 = Segment(R_1, Ws45)
Ws39: Wt39 + (0, hi)
s37 = Segment(R_1, Ws37)
Ws41: Wt41 + (0, hi)
s39 = Segment(R_1, Ws39)
Ws38: Wt38 + (0, hi)
s41 = Segment(R_1, Ws41)
Ws40: Wt40 + (0, hi)
s38 = Segment(R_1, Ws38)
Ws44: Wt44 + (0, hi)
s40 = Segment(R_1, Ws40)
s44 = Segment(R_1, Ws44)
Wt46 = (8.1, 0.9400000000000001)
Wt47 = (7.66, 0.38)
Wt48 = (8.78, 1.06)
Wt49 = (9.42, 0.78)
Wt50 = (8.3, 0.2)
Wt51 = (8.98, 0.18)
Wt52 = (8.120000000000001, -0.52)
Wt53 = (9.64, -0.04)
Wt54 = (8.84, -0.62)
Wt55 = (3.06, 1.18)
Wt56 = (2.4, 0.66)
Wt57 = (3.2800000000000002, 0.44)
Wt58 = (2.62, -0.1)
Wt59 = (2.3000000000000003, 1.48)
Wt60 = (1.5, 1.44)
Wt61 = (1.6, 0.62)
Wt62 = (1.8, -0.14)
Wt63 = (2.12, -0.86)
Wt64 = (13.040000000000001, 1)
Wt65 = (12.3, 1.18)
Wt66 = (13.8, 0.8200000000000001)
Wt67 = (13.16, 0.22)
Wt68 = (12.4, 0.42)
Wt69 = (11.540000000000001, 1.2)
Wt70 = (13.92, 0)
Wt71 = (11.64, 0.46)
Wt72 = (12.44, -0.38)
Ws46: Wt46 + (0, hd)
Ws47: Wt47 + (0, hd)
Ws48: Wt48 + (0, hd)
Ws49: Wt49 + (0, hd)
Ws50: Wt50 + (0, hd)
Ws51: Wt51 + (0, hd)
Ws52: Wt52 + (0, hd)
Ws53: Wt53 + (0, hd)
Ws54: Wt54 + (0, hd)
Ws64: Wt64 + (0, hd)
Ws65: Wt65 + (0, hd)
Ws66: Wt66 + (0, hd)
Ws67: Wt67 + (0, hd)
Ws68: Wt68 + (0, hd)
Ws69: Wt69 + (0, hd)
Ws70: Wt70 + (0, hd)
Ws71: Wt71 + (0, hd)
Ws72: Wt72 + (0, hd)
s46 = Segment(W_1, Ws46)
s47 = Segment(W_1, Ws47)
s48 = Segment(W_1, Ws48)
s49 = Segment(W_1, Ws49)
s50 = Segment(W_1, Ws50)
s51 = Segment(W_1, Ws51)
s52 = Segment(W_1, Ws52)
s53 = Segment(W_1, Ws53)
s54 = Segment(W_1, Ws54)
Ws55: Wt55 + (0, hi)
Ws56: Wt56 + (0, hi)
Ws57: Wt57 + (0, hi)
Ws58: Wt58 + (0, hi)
Ws59: Wt59 + (0, hi)
Ws60: Wt60 + (0, hi)
Ws61: Wt61 + (0, hi)
Ws62: Wt62 + (0, hi)
Ws63: Wt63 + (0, hi)
s55 = Segment(Ws55, S_1)
s56 = Segment(Ws56, S_1)
s57 = Segment(Ws57, S_1)
s58 = Segment(Ws58, S_1)
s59 = Segment(Ws59, S_1)
s60 = Segment(Ws60, S_1)
s61 = Segment(Ws61, S_1)
s62 = Segment(Ws62, S_1)
s63 = Segment(Ws63, S_1)
s64 = Segment(Ws64, Z_1)
s65 = Segment(Ws65, Z_1)
s66 = Segment(Ws66, Z_1)
s67 = Segment(Ws67, Z_1)
s68 = Segment(Ws68, Z_1)
s69 = Segment(Ws69, Z_1)
s70 = Segment(Ws70, Z_1)
s71 = Segment(Ws71, Z_1)
s72 = Segment(Ws72, Z_1)
texto1: "" + (If[nx1 ≟ 1, "", If[nx1 ≟ -1, "-", "" + nx1]]) + " x"
texto2: "" + (If[nx3 ≟ 1, "", If[nx3 ≟ -1, "-", "" + nx3]]) + " x"
texto7: "" + (If[a ≟ 1 ∨ a ≟ 0, "", If[a ≟ -1, "-", "" + a]]) + (If[a ≟ 0, "", "\;x\;"]) + (If[(b ≠ 0) ∧ ((a ≠ 0) ∨ (b  <  0)), If[b ≟ 0, "", If[b > 0, "+", "-"]], ""]) + (If[b ≠ 0, "" + "\;" + (abs(b)), If[b ≟ 0 ∧ a ≟ 0, "0", ""]]) + "\;=\;" + (If[c ≟ 1 ∨ c ≟ 0, "", If[c ≟ -1, "-", "" + c]]) + (If[c ≟ 0, "", "\;x\;"]) + (If[(d ≠ 0) ∧ ((c ≠ 0) ∨ (d  <  0)), If[d ≟ 0, "", If[d > 0, "+", "-"]], ""]) + (If[d ≠ 0, "" + "\;" + (abs(d)), If[d ≟ 0 ∧ c ≟ 0, "0", ""]]) + "\;\;" + (If[(nx1 ≠ nx3) ∧ ((nx1 ≠ a) ∨ (nx2 ≠ b) ∨ (nx3 ≠ c) ∨ (nx4 ≠ d)) ∧ pI ≟ pD, texto3 + "\;\;" + texto8, ""]) + "\;\;" + (If[B1 ≟ sol ∧ ((nx1 ≠ 1) ∨ (nx2 ≠ 0)), texto3 + "\;\;x\;=\;" + (FractionText[B1]), ""])