Question

Solve the following inequation, write the solution set and represent it on the number line.$$-3 (x - 7)\geq 15 - 7x > \dfrac {x + 1}{3}, x\in R$$

Solution

Given: $$-3(x - 7)\geq 15 - 7x > \dfrac {x + 1}{3}$$$$-3x + 21\geq 15 - 7x > \dfrac {x + 1}{3}$$$$\Rightarrow -3x + 21 \geq 15 - 7x$$ and $$155 - 7x > \dfrac {x + 1}{3}$$$$\Rightarrow 4x \geq -6$$ and $$45 - 21x > x + 1$$$$\Rightarrow x \geq - \dfrac {3}{2}$$ and $$44 > 22x$$$$\Rightarrow x \geq \dfrac {-3}{2}$$ and $$2 > x$$$$\therefore$$ Solution set $$= \left \{x : x \in R, \dfrac {-3}{2} \leq x < 2\right \}$$Mathematics

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