`3x +2 gt 5`
`-2x+8 gt -10`
Which of the following describes the range of x ?

Options

A. `x gt 1`
B. `x gt 9`
C. ` -1 lt x lt 9`
D. ` 9 gt x gt 1`

Answer

D

Explanation

Isolate x in each of the given inequalities, thten consider the results in combination. For `3x +2 gt 5,` subtract 2 from each side to get `3x gt 3, ` which means that `x fr 1.` For `-2x + 8 gt -10,` subtract 8 from each side to get `-2x gt-18.` Divided each side by -2, which means that you have to flip the inequality by -2, which means that you have to flip the inequality sign to get `x lt 9.` Taking thet two inequalities together, x must be greater than 1 but less than 9. This can be expressed as `1 lt x lt 9` or , alternatively, `9 gt x gt 1.` (D) is correct.