Solve the following system of linear inequalities and represent the solution graphically on a number line:
$3x - 7 > 2(x - 6), 6 - x > 11 - 2x$
$3x - 7 > 2(x - 6), 6 - x > 11 - 2x$
(N/A) First,solve the first inequality:
$3x - 7 > 2(x - 6)$
$3x - 7 > 2x - 12$
$3x - 2x > -12 + 7$
$x > -5$ ..... $(1)$
Next,solve the second inequality:
$6 - x > 11 - 2x$
$-x + 2x > 11 - 6$
$x > 5$ ..... $(2)$
From $(1)$ and $(2)$,the common solution is the intersection of the two intervals,which is $x > 5$.
Thus,the solution set is $(5, \infty)$.
The graphical representation on the number line is shown below:
$3x - 7 > 2(x - 6)$
$3x - 7 > 2x - 12$
$3x - 2x > -12 + 7$
$x > -5$ ..... $(1)$
Next,solve the second inequality:
$6 - x > 11 - 2x$
$-x + 2x > 11 - 6$
$x > 5$ ..... $(2)$
From $(1)$ and $(2)$,the common solution is the intersection of the two intervals,which is $x > 5$.
Thus,the solution set is $(5, \infty)$.
The graphical representation on the number line is shown below:
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