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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities

Solve $5 x-3 < 7 $ when (i) x is an integer (ii) x is a real number

1 Answer

  • 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 inequalities is $5x-3 < 7$
Adding same quantity +3 to both sides $=> 5x-3+3 < 7+3$
=> $ 5x <10$
Dividing by same positive quantities on both sides,
=> $ \large\frac{5x}{5} < \frac{10}{5}$
=> $ x < 2$
Step 2:
The integer less than 2 are ,
The solution set is ,
$\{ ....,-5,-4,-3,-2,-1,0,1\}$
Step 3:
when x is a real number all real number less than 2 satisfy the inequality .
The solution set is $ x \in (- \infty ,2)$
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