Question

Solve the given inequality: $-5\le 3x-2<7$, where $xϵR$

• A. $-1\le x<3$
• B. $-1\le x<2$
• C. $-2\le x<3$
• D. None

Answer 1

The correct option is A $-1\le x<3$

The given inquations are

$-5\le 3x-2<\mathrm{7..........}\left(ii\right)$

$\left(i\right)⟶-5\le 3x-2⟹-5+2\le 3x⟹-3\le 3x⟹-1\le x.$

Again

$\left(ii\right)⟶3x-2<7⟹3x<7+2⟹3x<9⟹x<3.$\\

$\therefore -1\le x<3.$