If \( x\in R \), the solution set of \( \displaystyle\frac{1}{5}x-\frac{3x-1}{2}\gt 2 \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \left(-\infty,-\displaystyle\frac{15}{13}\right) \)
Multiplying both sides by 10, a positive number, keeps the inequality:
\( \displaystyle 2x-5(3x-1)\gt 20 \)
\( \displaystyle 2x-15x+5\gt 20 \)
\( \displaystyle -13x\gt 15 \)
Dividing by a negative number reverses the sign:
\( \displaystyle x\lt-\frac{15}{13} \)
The inequality is strict, so the end point is not included: \( x\in\left(-\infty,-\frac{15}{13}\right) \).