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# Solve the inequalities and represent the solution graphically on number line. $3x-7 > 2(x-6) ; 6-x > 11-2x$

$\begin{array}{1 1}(A)\;(5,\infty) \\(B)\;(-5,5)\\(C)\;(-23,2]\\(D)\;[2,3]\end{array}$

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 $'>'$ .
• 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 first inequality is $3x-7 > 2(x-6)$
$=> 3x-7 > 2x-12$
Adding 7 to both sides of inequality subtracting 2x from both sides of inequality
$=> 3x-7+7 -2x > 2x _12 +7 -2x$
$=> x > -5$
Step 2:
The second inequality is $6-x > 11-2x$
Subtracting 6 from both sides of inequality adding 2x to both sides of inequality $6-x-6 +2x > 11-2x -6 +2x$
$x >5$-----(2)
Step 3:
From (1) and (2) we conclude that all numbers greater than -1 and greater than 5 from the common solution for the given set of inequalities.
The solution set is $(5, \infty)$
The solution is represented graphically as the number line as