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Linear Inequations — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLinear Inequations2 Marks
Question
Solve the following linear inequations in R:
Solve: -4x > 30, when
  1. $\text{x}\in\text{R}$
  2. $\text{x}\in\text{Z}$
  3. $\text{x}\in\text{N}$
✓

Answer

Now, -4x > 30
$\Rightarrow\text{x}<\frac{-30}{4}=\frac{-15}{2}$
  1. If $\text{x}\in\text{R},$ then $\text{x}<\frac{-15}{2}\Rightarrow\text{x}\in\Big(-\infty,-\frac{15}{2}\Big)$
  2. If $\text{x}\in\text{R},$ then $\text{x}<-\frac{15}{2}\Rightarrow\text{x}\in\{...,-10,-9-8\}$
  3. $-4\text{x}>30$
$\Rightarrow-\text{x}>\frac{30}{4}$

$\Rightarrow\text{x}<-\frac{30}{4}$

As $\text{x}\in\text{R},$ so x cannot be less than 1.

$\therefore$ The solution set of the inequality -4x > 30 is null set $\phi$

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