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Home  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Solve the given inequality graphically in two, dimensional plane . $ x > -3$

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Toolbox:
  • To represent the solution of linear inequality of one or two variable in a plane if the inequality involves $'\geq'$ or $' \leq$ we draw the graph of the line as a thick line to indicate the line is included in the solution set.
  • If the inequality involves $'>'$ as $'<'$ we draw the graph of the line using is not included in the solution set.
  • To solve an inequality $ax+by > c \qquad a \neq 0, b \neq 0 ( or \;> )$
  • We consider the corresponding equation $ax+by =c$ which represents a straight line This line divides the plane into two half planes I and II
  • We take any point in I half plane and check if it satisfies the given inequality will be one half plane (called solution region ) Containing the point satisfying the inequality
The given inequality is $ x > -3$
Consider the equation $x=-3$
It is represented by the dotted line as shown,
Step 2:
The line divides the XY plane into two half planes I and II consider a point 90,0) in the half plane II
We see that $ 0 > -3$ is true.
Step 3:
Therefore the half plane I is not the solution region.
The solution region of the given inequality in the half plane II excluding the line.
It is represented by the shaded region.
answered Jul 30, 2014 by meena.p
 
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