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

Answer 1

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)$