Question

Which number line represents the solution set for the inequality - 2x2 4? -10 -8 6 -4 -20 2 4 6 8 10 -10 -8 6 + -2 0 2 -4 6 + -10 -8 6 -4 -2 0 2 68 10 -10 -8 -6 -4 -2 0 6 810​

Answer 1

`- (1)/(2) x \geqslant 4 \\ - x \geqslant 2 * 4 \\ - x \geqslant 8 \\ \boxed{\ x \leqslant - 8}`

x→{-∞,-8]

Number line :---

Arrow which represents solid sphere directed from (-8) moving towards left (-∞) will be the answer

2nd one is the right answer.

Answer 2

Option (2)

Explanation:

Given inequality is,

`-(1)/(2)x\geq 4`

⇒
`(1)/(2)x\leq -4`

⇒ x ≤ -8

When we plot this inequality on a number line,

An arrow starting with a solid point from x = -8 and arrow directing towards negative numbers will represent the given inequality.

Option (2) will be the answer.