3(x – 1) < -3(2 – 2x)? A) x > 1 B) x < 1 C) x > -1 D) x < -1

1 Answer
Mar 27, 2016

Answer:

#"B": x<1#

Explanation:

The given problem is:

#3(x-1)<-3(2-2x)#

The solutions are:

#"A")color(white)(i)x>1#
#"B")color(white)(i)x<1#
#"C")color(white)(i)x>##-1#
#"D")color(white)(i)x<-1#

Solving the Inequality
#1#. Start by factoring #-2# from the bracketed terms on the right-hand side of the equation.

#3(x-1)<-3(2-2x)#

#3(x-1)<-3*-2(-1+x)#

#2#. Multiply #-3# and #-2# together on the right-hand side of the equation.

#3(x-1)<6(1-x)#

#3#. Divide both sides by #6#.

#(3(x-1))/6<(6(1-x))/6#

#(color(red)cancelcolor(black)3^1(x-1))/color(red)cancelcolor(black)6^2<(color(red)cancelcolor(black)6^1(1-x))/color(red)cancelcolor(black)6^1#

#(x-1)/2<1-x#

#4#. Multiply the whole inequality by #2# to get rid of the denominator.

#2((x-1)/2)<2(1-x)#

#color(red)cancelcolor(black)2^1((x-1)/color(red)cancelcolor(black)2^1)<2(1-x)#

#x-1<2-2x#

#5#. Add #2x# to both sides of the equation.

#x# #color(red)(+2x)-1<2-2x# #color(red)(+2x)#

#3x-1<2#

#6#. Add #1# to both sides of the equation.

#3x-1# #color(red)(+1)<2# #color(red)(+1)#

#3x<3#

#7#. Divide both sides by #3#.

#(3x)/3<3/3#

#color(green)(|bar(ul(color(white)(a/a)x<1color(white)(a/a)|)))#