Question 4(ii)Solve the following inequation, write the solution set and represent it on the real number line.5x - 21

Question

Question 4(ii)Solve the following inequation, write the solution set and represent it on the real number line.5x - 21 < 5x7−6≤−337+x\dfrac{5x}{7} - 6 \le -3\dfrac{3}{7} + x75x​−6≤−373​+x, x ∈ R.

Accepted Answer

Given, inequation : 5x - 21 < 5x7−6≤−337+x\dfrac{5x}{7} - 6 \le -3\dfrac{3}{7} + x75x​−6≤−373​+xSolving L.H.S. of the inequation :⇒5x−21<5x7−6⇒5x−5x7<21−6⇒35x−5x7<15⇒30x7<15⇒x<7×1530⇒x<72 ..........(1)\Rightarrow 5x - 21 \lt \dfrac{5x}{7} - 6\[1em] \Rightarrow 5x - \dfrac{5x}{7} \lt 21 - 6 \[1em] \Rightarrow \dfrac{35x - 5x}{7} \lt 15 \[1em] \Rightarrow \dfrac{30x}{7} \lt 15 \[1em] \Rightarrow x \lt \dfrac{7 \times 15}{30} \[1em] \Rightarrow x \lt \dfrac{7}{2} \text{ ..........(1)}⇒5x−21<75x​−6⇒5x−75x​<21−6⇒735x−5x​<15⇒730x​<15⇒x<307×15​⇒x<27​ ..........(1)Solving R.H.S. of the inequation :⇒5x7−6≤−337+x⇒5x7−6≤−247+x⇒x−5x7≥−6+247⇒7x−5x7≥−42+247⇒2x7≥−187⇒2x≥−18⇒x≥−182⇒x≥−9 ..........(2)\Rightarrow \dfrac{5x}{7} - 6 \le -3\dfrac{3}{7} + x \[1em] \Rightarrow \dfrac{5x}{7} - 6 \le -\dfrac{24}{7} + x \[1em] \Rightarrow x - \dfrac{5x}{7} \ge -6 + \dfrac{24}{7} \[1em] \Rightarrow \dfrac{7x - 5x}{7} \ge \dfrac{-42 + 24}{7} \[1em] \Rightarrow \dfrac{2x}{7} \ge \dfrac{-18}{7} \[1em] \Rightarrow 2x \ge -18 \[1em] \Rightarrow x \ge \dfrac{-18}{2} \[1em] \Rightarrow x \ge -9 \text{ ..........(2)}⇒75x​−6≤−373​+x⇒75x​−6≤−724​+x⇒x−75x​≥−6+724​⇒77x−5x​≥7−42+24​⇒72x​≥7−18​⇒2x≥−18⇒x≥2−18​⇒x≥−9 ..........(2)From equation (1) and (2),Solution set = {x : -9 ≤ x < 72\dfrac{7}{2}27​, x ∈ R}Hence, solution set = {x : -9 ≤ x < 72\dfrac{7}{2}27​, x ∈ R}.

Solved 2025 Specimen Paper ICSE Class 10 Mathematics — Question 2

Question 4(ii)