Solve the following linear inequations in R – 4x > 30, when i. x �

1.	Solve the following linear inequations in R – 4x > 30, when i. x ∈ R ii. x ∈ Z iii. x ∈ N
Answer» Given, –4x > 30 ⇒ \(-\frac{4x}{4}\) > \(\frac{30}{4}\) ⇒ - x > \(\frac{15}{2}\) ∴ x < \(-\frac{15}{2}\) i. x ∈ R When x is a real number, the solution of the given inequation is (-∞,\(-\frac{15}{2}\)). ii. x ∈ Z As - 8 < \(-\frac{15}{2}\) < -7, When x is an integer, the maximum possible value of x is –8. Thus, 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 ∅.

Solve the following linear inequations in R – 4x > 30, when i. x ∈ R ii. x ∈ Z iii. x ∈ N

Answer»

Given,

–4x > 30

⇒ \(-\frac{4x}{4}\) > \(\frac{30}{4}\)

⇒ - x > \(\frac{15}{2}\)

∴ x < \(-\frac{15}{2}\)

i. x ∈ R

When x is a real number, the solution of the given inequation is (-∞,\(-\frac{15}{2}\)).

ii. x ∈ Z

As - 8 < \(-\frac{15}{2}\) < -7,

When x is an integer, the maximum possible value of x is –8.

Thus,

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 ∅.