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

1 Answer
Mar 27, 2016

"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)|)))