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# Solve the inequality $-3 \leq 4 - \large\frac{7x}{2} $$\leq 18 \begin{array}{1 1}(A)\;[2,8]\\(B)\;[-4,2]\\(C)\;[3,4]\\(D)\;[2,3]\end{array} Can you answer this question? ## 1 Answer 0 votes Toolbox: • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality. • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality. • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e '>' sign changes to '<' and '<' changes '>' . Step 1: The given inequality is -3 \leq 4 - \large\frac{7x}{2}$$ \leq 18$
Adding -4 through out the inequality $=> -3-4 \leq 4 - \large\frac{7x}{2} $$-4 \leq 18-4 => -7 \leq \large\frac{-7x}{2}$$ \leq 14$
Multiplying by a negative number -2 through out
$=> 14 \geq 7x \geq -28$
Dividing by 7 through out the inequality => $2 \geq x \geq -4$
Step 2:
All numbers less than or equal to 2 and greater than or equal to -4 are solutions to given inequality .
The solution set is $[-4,2]$
Hence B is the correct answer.