COMEDK · Maths · 1. Basic of Mathematics
The solution set of the system of inequalities \(5-4 x \leq-7\) or \(5-4 x \geq 7, x \in R\) is
- A \(\left(-\infty,-\dfrac{1}{2}\right) \cup(3, \infty)\)
- B \(\left(-\infty,-\dfrac{1}{2}\right] \cup[3, \infty)\)
- C \(\left(-\infty,-\dfrac{1}{2}\right] \cap(3, \infty)\)
- D \(\left(-\infty,-\dfrac{1}{2}\right) \cap[3, \infty)\)
Answer & Solution
Correct Answer
(B) \(\left(-\infty,-\dfrac{1}{2}\right] \cup[3, \infty)\)
Step-by-step Solution
Detailed explanation
The given system of inequalities is \(5 - 4x \leq -7\) or \(5 - 4x \geq 7\). Solving the first inequality: \(5 - 4x \leq -7\) \(-4x \leq -7 - 5\) \(-4x \leq -12\) Dividing by \(-4\) reverses the inequality sign: \(x \geq \dfrac{-12}{-4}\) \(x \geq 3\) Solving the second…
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