Question

Chapter 6: Review page 2

For problems 7, 8 and 9, determine whether each of the numbers is a solution to the
inequality.
3x2 < 2 - 2x. (Yes or No)
7) 1
9)
113
8) 1/2

Answer 1

7) No

8) Yes

9) Yes

Explanation:

Plug each possible solution into the inequality and see if it holds true:

If x=1 (Not a solution)

`\displaystyle 3(1)-2\stackrel{?}{ < }2-2(1)\\3-2\stackrel{?}{ < }2-2\\1\\less0`

If x=1/2 (Is a solution)

`\displaystyle 3\biggr((1)/(2)\biggr)-2\stackrel{?}{ < }2-2\biggr((1)/(2)\biggr)\\(3)/(2)-2\stackrel{?}{ < }2-1\\\\(1)/(2) < 1`

If x=1/3 (Is a solution)

`\displaystyle 3\biggr((1)/(3)\biggr)-2\stackrel{?}{ < }2-2\biggr((1)/(3)\biggr)\\1-2\stackrel{?}{ < }2-(2)/(3)\\\\-1 < (4)/(3)`