3(x – 1) < -3(2 – 2x)? A) x > 1 B) x < 1 C) x > -1 D) x < -1
1 Answer
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
#3(x-1)<-3(2-2x)#
#3(x-1)<-3*-2(-1+x)#
#3(x-1)<6(1-x)#
#(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#
#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#
#x# #color(red)(+2x)-1<2-2x# #color(red)(+2x)#
#3x-1<2#
#3x-1# #color(red)(+1)<2# #color(red)(+1)#
#3x<3#
#(3x)/3<3/3#
#color(green)(|bar(ul(color(white)(a/a)x<1color(white)(a/a)|)))#