Wat is de waarde van x, gegeven dat (x + 3) / (x + 7)> 3?

Antwoord:

De oplossing is #x in (-9, -7) #

Uitleg:

Je kunt niet oversteken

De ongelijkheid is

# (X + 3) / (x + 7)> 3 #

#=>#, # (X + 3) / (x + 7) -3> 0 #

#=>#, # (X + 3/3 (x + 7)) / (x + 7) #

#=>#, # (X + 3-3x-21) / (x + 7)> 0 #

#=>#, # (- 2x-18) / (x + 7)> 0 #

#=>#, # (2 (x + 9)) / (x + 7) <0 #

Laat #f (x) = (2 (x + 9)) / (x + 7) #

Laten we een tekenkaart bouwen

#color (wit) (aaaa) ##X##color (wit) (aaaa) ## -Oo ##color (wit) (aaaa) ##-9##color (wit) (aaaa) ##-7##color (wit) (aaaa) ## + Oo #

#color (wit) (aaaa) ## X + 9 ##color (wit) (aaaaaa) ##-##color (wit) (aaaa) ##+##color (wit) (aaaa) ##+#

#color (wit) (aaaa) ## X + 7 ##color (wit) (aaaaaa) ##-##color (wit) (aaaa) ##-##color (wit) (aaaa) ##+#

#color (wit) (aaaa) ##f (x) ##color (wit) (AAAAAAA) ##+##color (wit) (aaaa) ##-##color (wit) (aaaa) ##+#

daarom

#f (x) <0 # wanneer #x in (-9, -7) #

grafiek {(x + 3) / (x + 7) -3 -26.83, 9.2, -8.96, 9.06}