How do you solve #-30x + 30\leq - 6( 4x - 12)#?

2 Answers
Jim G.
May 10, 2018

#x>=-7#

Explanation:

#"distribute parenthesis on right side of inequality"#

#-30x+30<= -24x+72#

#"add "24x" to both sides"#

#-30x+24x+30<=cancel(-24x)cancel(+24x)+72#

#rArr-6x+30<=72#

#"subtract 30 from both sides"#

#-6xcancel(+30)cancel(-30)<=72-30#

#rArr-6x<=42#

#"divide both sides by "-6#

#color(blue)"reversing the sign as a consequence"#

#rArrx>= -7#

#x in[-7,oo)larrcolor(blue)"in interval notation"#

Binayaka C.
May 10, 2018

Solution: # x >= -7 or x in [-7, oo)#

Explanation:

# -30 x + 30 <= -6( 4 x-12)# or

# -30 x + 30 <= -24 x +72# or

# -30 x + 24 x <= 72 -30# or

# -6 x <= 42 # or

#-x <= 7# or

#x >= -7 #

Solution: # x >= -7 or x in [-7, oo)#[Ans]

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