Question

Phyllis solved the compound inequality 16 < 2(3x – 1) < 28. She began by first breaking the inequality into two separate inequalities, then she correctly solved each for x. 16 < 2(3x – 1) and 2(3x – 1) < 28 3 < x x < 5 Which graph represents her solution?

Answer 1

16<2(3x-1)<28  divide all terms by 2

8<3x-1<14  add 1 to all terms

9<3x<15  divide all terms by 3

3<x<5

x=(3,5) in interval notation

On a number line, it would be a line segment from 3 to 5 with open circles at 3 and 5.

On a coordinate system graph, it would be an infinitely high shaded plane between the vertical lines x=3 and x=5

Answer 2

From question ,
16<2(3x-1)=16<6x-2
                 =16+2<6x-2+2
                 =18<6x
                 =18/6<6x/6
                 =3<x
Again,
2(3x-1)<28
=6x-2<28
=6x-2+2<28+2
=6x<30
=6x/6<30/6
=x<5
So both of ther graphs 3<x and x<5 represents her solution