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Q)

Solve the given inequality and show the graph of the solution on number line: $3(1-x) <2 (x +4)$ Comment
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 $3(1-x) < 2( x+4)$
=> $3-3x < 2x+8$
Adding -8 and 3x on both sides of the inequality.
$=> 3-8 < 2x +3x$
$=> -5 < 5x$
Dividing both sides of the inequality by a positive number 5.
$=> \large\frac{-5}{5} < \frac{5x}{5}$
$=> -1 < x$
Step 2:
All numbers greater than -1 represent the solution of the given inequality .
The solution set is $(-1, \infty)$
The graphical representation on the number line is