Question

If -2 < x ≤ 3 then find the interval in which 2-3x lies.​

Answer 1

it is given that -2 < x ≤ 3 then we have to find the interval in which 2 - 3x lies

-2 < x ≤ 3

when we change sign of x, sign of inequality change as shown below.

a ≤ x ≤ b ⇒-a ≥ -x ≥ - b

so, -2 < x ≤ 3 ⇒-(-2) > -x ≥ -3

⇒2 > -x ≥ -3

⇒-3 ≤ -x < 2

⇒ -3 × 3 ≤ -3x < 3 × 2

⇒-9 ≤ -3x < 6

⇒2 - 9 ≤ 2 - 3x < 2 + 6

⇒-7 ≤ 2 - 3x < 8

therefore, [-7, 8) is the interval in which 2 - 3x lies.

Answer 2

$- 2 < x \leqslant 3$

$a \leqslant x \leqslant b↬-a \geqslant - x \geqslant - b$

$- 2 > - x > - 3$

$- 3 \leqslant - x \leqslant 2$

$- 3 \times 3 \leqslant - 3x < 3 \times 2$

$- 9 \leqslant - 3x < 6$

$2 - 9 \leqslant 2 - 3x < 2 + 6$

$- 7 \leqslant 2 - 3x < 8$

$( - 7 \: 8) \: is \: the \: interval \: in \: which \: 2 - 3x \: lies$