Question

If x E{-2,-1,0,1,2,3,4,5}, find the solution set of each of the following inequations: (i) 3x + 4 < 15 (i) 2/3 +x - 1/6 please answer my question I will mark you as brilliant please it's urgent ​ We are given two inequalities which has the solution that belongs to { -2, -1, 0, 1, 2, 3, 4, 5 } Inequality (i) ⇒ 3x + 4 < 15 ⇒ 3x < 11 ⇒ x < 11/3 ⇒ x < 3.666... Which means every value of x which is less than 3.6 satisfies the given inequality, but it is given in the question that x must belong to the given set of solutions. So, We have the following solution ⇒ x ∈ { -2, -1, 0, 1, 2, 3 } Inequality (ii) ⇒ 2/3 + x < 1/6 ⇒ x < 1/6 - 2/3 ⇒ x < (1 - 4)/6 ⇒ x < -3/6 ⇒ x < -0.5 Which means every value of x less than -0.5 satisfies the given inequality. But x must belong to { -2, -1, 0, 1, 2, 3, 4, 5 }, so numb


Pls solve it

Answer 1

Solution : -

We have 3x - 5 < 4

⇒ 3x - 5 + 5 < 4 + 5 (Add 5 to both sides)

⇒ 3x < 9

⇒ 3x/3 < 9/3 (Divide both sides by 3)

⇒ x < 3

So, the replacement set = {1, 2, 3, 4, 5, ...}

Therefore, the solution set = {1, 2} or S = {x : x ∈ N, x < 3}

Let us mark the solution set graphically.

Image

Solution set is marked on the number line by dots.

Answer 2

Answer:

i) ans is -2,-1,0,1,2,3

ii) ans is -2, -1, 0, 1, 2, 3, 4, 5

Explanation:

in first case we need to take no. less than 3.6

and in second one we need to take no. less than -0.5

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