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ICSEClass 10MathematicsLinear Inequations03 Mark2025 Hard

QQuestion

Solve the inequation, write the solution set and represent it on the real number line:

2x − \frac{5}{3} < \frac{3\mathrm{x}}{5} + 10 ≤ \frac{4\mathrm{x}}{5} + 11, x ∈ R.

Exam-ready answer • 03 Mark

Answer

Solving the left-hand part:

2x − \frac{5}{3} < \frac{3\mathrm{x}}{5} + 10

\frac{6\mathrm{x}-5}{3}<\frac{3\mathrm{x}+50}{5}

Multiplying by 15:

5(6x − 5) < 3(3x + 50)

⇒ 30x − 25 < 9x + 150

⇒ 21x < 175

⇒ x < \frac{25}{3} … (1)

Solving the right-hand part:

\frac{3\mathrm{x}}{5} + 10 ≤ \frac{4\mathrm{x}}{5} + 11

⇒ 3x + 50 ≤ 4x + 55

⇒ x ≥ −5 … (2)

Combining (1) and (2):

−5 ≤ x < \frac{25}{3}

Therefore, the solution set is [−5, \frac{25}{3}).

On the number line, use a closed point at −5, an open point at \frac{25}{3}, and shade between them.

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