Linear Inequalities — Maths STD 11 Science — Question
CBSE BoardEnglish MediumSTD 11 ScienceMathsLinear Inequalities2 Marks
Question
Solve the inequality: $-3 \leq 4-\frac{7 x}{2} \leq 18$
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Answer
Given inequality $-3 \leq 4-\frac{7 x}{2} \leq 18$ $\Rightarrow-3 \leq 4-\frac{7 x}{2} \leq 18$ $\Rightarrow-3-4 \leq 4-\frac{7 x}{2}-4 \leq 18-4$ $\Rightarrow-7 \leq-\frac{7 x}{2} \leq 14$ Multiplying the inequality by -2. $\Rightarrow$ (-7) $\times$ (-2) $\geq-\frac{7 x}{2} \times(-2) \geq 14 \times$ (-2) $\Rightarrow$ 14 $\ge$ 7x $\ge$ -28 $\Rightarrow$ -28 $\le$ 7x $\le$ 14 Dividing the inequality by 7 $\Rightarrow$ -4 $\le$ x $\le$ 2 $\therefore$ all real numbers x greater than or equal to -4 but less than or equal to 2 are the solution of given equality. x $\in$ [-4, 2] solution set =[-4,2]
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