The two inequalities must be verified at the same time. Let's take into account the first one:
\(\frac{5x - 1}{x + 3}< 1\)
\(\frac{5x - 1 - x - 3}{x + 3} < 0\)
\(\frac{4x - 4}{x + 3} < 0\)
\(Numerator: x ≥ 1\)
\(Denominator: x > - 3\)
So, it will be negative in the range \((-3,1]\)
Let's consider the second one:
\(|2x - 5| ≤ 5\)
\(-5 ≤ 2x - 5 ≤ 5\)
\(0 ≤ x ≤ 5\)
So, the range is \([0, 5]\)
Put these outputs together to assess the values for which \(x\) is verified in both.
This happens when \(0 ≤ x ≤ 1\)
You reject all options except
C.
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