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)|)))