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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Q)

Solve $-12 x > 30$ when (i) x is a natural number (ii) x is an integer

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A)
Toolbox:
  • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
  • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
  • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .
Step 1:
The given in equalities
$-12 x > 30$
Dividing both sides by negative number $-12$
=> $ \large\frac{-12 x}{-12} < \frac{30}{-12}$
=> $ x < \large\frac{-5}{2}$
Step 2:
There is no natural number less than $\large\frac{-5}{2}$
Step 3:
The integer less than $ \large\frac{-5}{2}$ are $.....-5,-4,-3$
The solution set is $ \{ ........,-5,-4,-3\}$
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