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Home  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Solve the given inequality and show the graph of the solution on number line: $ 3x-2 <2 x +1$

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  • 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
answered Jul 26, 2014 by meena.p
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