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ICSE Class X Math 2016 Paper

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Question : 8 of 57
Marks: +1, -0
Solve the following inequation, write the solution set and represent it on the number line.
−3(x−7)≥15−7x>  x+13,x∈R-3(x-7) \ge 15-7x > \; \frac{x+1}{3}, x \in R
Solution:  
Given : −3(x−7)≥15−7x>  x+13-3(x-7) \ge 15-7x > \; \frac{x+1}{3}
  −3x+21≥15−7x>  x+13\; -3x+21 \ge 15-7x > \; \frac{x+1}{3}
  ⇒−3x+21≥15−7x\; \Rightarrow -3x+21 \ge 15-7x and 15−7x>  x+1315-7x > \; \frac{x+1}{3}
  ⇒    4x≥−6\; \Rightarrow \; \; 4x \ge -6 and 45−21x>x+145-21x > x+1
  ⇒    x≥−32   and   44>22x\; \Rightarrow \; \; x \ge -\frac{3}{2} \; \text{ and } \; 44 > 22x
  ⇒    x≥−32   and     2>x\; \Rightarrow \; \; x \ge \frac{-3}{2} \; \text{ and } \; \; 2 > x
∴ Solution set ={x:x∈R,  −32≤x<2}= \{ x: x \in R, \; \frac{-3}{2} \le x < 2 \}
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