Question

Find the solution set of the given inequation and represent this set on number line: 4 < -(x + 2) < 9,x € I​

Answer 1

Answer:

Step-by-step explanation:

4x - 19 < 3x/5 – 2 ≤ -2/5 + x, x ∈ R

∴ 4x – 19 < 3x/5 – 2,

4x – 3x/5 < -2 + 19,

17x/5 < 17,

x < 5,

and 3x/5 – 2 ≤ -2/5 + x

3x/5 – x ≤ -2/5 + 2

-2x ≤ 8

x ≥ - 4

⇒ -4 ≤ x < 5

Answer 2

4< -(x+2)<9

=> 4< -x-2

=> -x> 4+2

=> -x > 6

=> x< -6. ( inverse property)

also, -(x+2)< 9

=> -x < 9+2

=> -x < 11

=> x > -11

so the solution set = {-10,-9,-8,-7}

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