Solve the following linear in equations in R.

Solve:-4x >30, when

(i) $x ϵ R$ (ii) $x ϵ Z$ (iii) $x ϵ N$

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Solution

Now, -4x > 30

$\Rightarrow x < \frac{- 30}{4} = \frac{- 15}{2} (i) I f x ϵ R, t h e n x < \frac{- 15}{2} \Rightarrow x ϵ (- \infty, - \frac{15}{2}) (i i) I f x ϵ Z, t h e n x < - \frac{15}{2} \Rightarrow x ϵ {. . ., - 10, - 9, - 8} (i i i) - 4 x > 30 \Rightarrow - x > \frac{30}{4} \Rightarrow x < - \frac{30}{4} A s x ϵ N, s o x c a n n o t b e l e s s t h a n 1. ∴ T h e s o l u t i o n s e t o f t h e i n e q u a l i t y - 4 x > 30 i s n u l l s e t ϕ .$

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