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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Q)

Solve the given inequality and show the graph of the solution on number line: $ 5x-3 < 3x -5$

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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 $'>'$ .
  • 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.
Step 1:
The given inequality is
$5x-3 \geq 3x-5$
Adding 3 and -3x on both sides of the inequality.
$=> 5x-3x \geq -5 +3$
$=> 2x \geq -2$
Dividing by positive number 2 on both sides.
$=> \large\frac{2x}{2} \geq \frac{-2}{2}$
$ x \geq -1$
Step 2 :
All number greater than or equal to -1 represent the solution of the given inequality.
The graphical representation on the number line is :
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