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

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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 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 ,
$...........-5,-4,-3,,-2,-1,0,1$
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 $x \in (- \infty ,2)$