# Solve the given inequality and show the graph of the solution on number line: $3x-2 <2 x +1$

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 $'>'$ .
• To represent solution of linear inequality involving one variable on a number line, if the inequality involves $\geq$ or $\leq$ are draw filled circle (0) on the number is included in the solution set.
• If the inequality involves $'>'$ or $'<'$ we draw open circle (0) on the number line to indicate the number is excluded from the solution set.
The given inequality is $3x-2 < 2x+1$
Adding +2 and -2x on both sides of the inequality .
=> $3x-2x <1+2$
$x <3$
Step 2:
All numbers less than 3 from the solution set for the given inequality $(-\infty,3)$
The graphical representation on the number line is