Given:
-4x > 30
So when we divide by 4, we get
\(\dfrac{-4x}{4} > \dfrac{30}{4}\)
-x > \( \dfrac{15}{2}\)
x < \( \dfrac{-15}{2}\)
(i) x ∈ R
When x is a real number, the solution of the given inequation is (-∞,\( \dfrac{-15}{2}\)).
(ii) x ∈ Z
When, -8 < \( \dfrac{-15}{2}\) < -7
So when, when x is an integer, the maximum possible value of x is -8.
The solution of the given inequation is {…, –11, –10, -9, -8}.
(iii) x ∈ N
As natural numbers start from 1 and can never be negative, when x is a natural number, the solution of the given inequation is ∅.
Answered by Aaryan | 1 year agoSolve each of the following in equations and represent the solution set on the number line \( \dfrac{5x}{4}-\dfrac{4x-1}{3}>1,\) where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line.\( \dfrac{5x-8}{3}\geq \dfrac{4x-7}{2}\), where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line. 3 – 2x ≥ 4x – 9, where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line. 3x – 4 > x + 6, where x ϵ R.
Solve each of the following in equations and represent the solution set on the number line. 5x + 2 < 17, where
(i) x ϵ Z,
(ii) x ϵ R.