(1)/abs(11-4x)=10

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Solution for (1)/abs(11-4x)=10 equation:


D( x )

abs(11-(4*x)) = 0

abs(11-(4*x)) = 0

abs(11-(4*x)) = 0

abs(11-4*x) = 0

abs(11-4*x) = 0

x in (-oo:+oo)

abs(11-4*x)

11-4*x >= 0

11-4*x >= 0 // - 11

-4*x >= -11 // : -4

x <= -11/(-4)

x <= 11/4

x in (-oo:11/4>

11-4*x = 0

x in (11/4:+oo)

-(11-4*x) = 0

abs(11-4*x) = 0

/| 11-4*x = 0 i x in (-oo:11/4>| -(11-4*x) = 0 i x in (11/4:+oo)

x in (-oo:11/4>

11-4*x = 0 // - 11

-4*x = -11 // : -4

x = -11/(-4)

x = 11/4

x in (11/4:+oo)

-(11-4*x) = 0

4*x-11 = 0 // + 11

4*x = 11 // : 4

x = 11/4

(11/4:+oo)

x in (-oo:11/4) U (11/4:+oo)

1/abs(11-(4*x)) = 10 // - 10

1/abs(11-(4*x))-10 = 0

1/abs(11-4*x)-10 = 0

1/abs(11-4*x)-10 = 0

x in (-oo:+oo)

abs(11-4*x)

11-4*x >= 0

11-4*x >= 0 // - 11

-4*x >= -11 // : -4

x <= -11/(-4)

x <= 11/4

x in (-oo:11/4>

1/(11-4*x)-10 = 0

x in (11/4:+oo)

1/(-(11-4*x))-10 = 0

1/abs(11-4*x)-10 = 0

/| 1/(11-4*x)-10 = 0 i x in (-oo:11/4>| 1/(-(11-4*x))-10 = 0 i x in (11/4:+oo)

x in (-oo:11/4>

1/(11-4*x)-10 = 0

1/(11-4*x)+(-10*(11-4*x))/(11-4*x) = 0

1-10*(11-4*x) = 0

40*x-109 = 0

(40*x-109)/(11-4*x) = 0

(40*x-109)/(11-4*x) = 0 // * 11-4*x

40*x-109 = 0

40*x-109 = 0 // + 109

40*x = 109 // : 40

x = 109/40

x in (11/4:+oo)

1/(-(11-4*x))-10 = 0

1/(4*x-11)-10 = 0

1/(4*x-11)+(-10*(4*x-11))/(4*x-11) = 0

1-10*(4*x-11) = 0

111-40*x = 0

(111-40*x)/(4*x-11) = 0

(111-40*x)/(4*x-11) = 0 // * 4*x-11

111-40*x = 0

111-40*x = 0 // - 111

-40*x = -111 // : -40

x = -111/(-40)

x = 111/40

x in { 109/40, 111/40 }

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