$\begin{array}{1 1}(A)\;[-7,11] \\(B)\;(-5,5)\\(C)\;(-23,2]\\(D)\;[2,3]\end{array} $

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- 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 first inequality is $5(2x-7)-3(2x+3) \leq 0$

$=> 10x -35-6x-9 \leq 0$

$=> 4x -44 \leq 0$

Adding 44 on both sides of the inequality

$ => 4x -44 +44 \leq 44$

$=> 4x \leq 44$

Divide both sides by positive number 4 .

$=> x \leq 11$------(1)

Step 2:

The second inequality is $2x +19 \leq 6x+47$

Adding -47 to both sides of inequality .

Adding -2x to both sides of inequality

$=> 2x+19-47 -2x \leq 6x +47 -47 -2x$

$=> 19-47 \leq 4x$

$ -28 \leq 4x$

Dividing by positive number 4 on both sides of inequality.

$-7 \leq x$ -----(2)

Step 3:

From (1) and (2) it can be conclude that all numbers greater than or eqaual to -7 and less than or equal to 11 are solutions to given system of inequalities

The solution set is $[-7,11]$

The solution is represented graphically as the number line as follows,

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