QQuestion
Solve the following inequation, write the solution set and represent it on the real number line.
−1 < \frac{2\mathrm{x}-3}{3} − \frac{\mathrm{x}}{5} ≤ 1, x ∈ R
ICSEClass XMathematicsLinear Inequations03 Mark2026 Easy
✓Answer
−1 < \frac{2\mathrm{x}-3}{3} − \frac{\mathrm{x}}{5} ≤ 1
Taking LCM 15:
−1 < \frac{10\mathrm{x}-15-3\mathrm{x}}{15} ≤ 1
⇒ −1 < \frac{7\mathrm{x}-15}{15} ≤ 1
Solving the left-hand inequality:
−15 < 7x − 15
⇒ 0 < 7x
⇒ x > 0
Solving the right-hand inequality:
7x − 15 ≤ 15
⇒ 7x ≤ 30
⇒ x ≤ \frac{30}{7}
Therefore, 0 < x ≤ \frac{30}{7}.
Solution set = \left(0,\frac{30}{7}\right]
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