Question

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

Answer 1

`"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)|)))`