Find the range of values of t which satisfies the inequality.
2t − 1 \(\leq\) 3 and 2− t \(\geq\) 5
2t − 1 \(\leq\) 3 and 2− t \(\geq\) 5
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Correct Answer: Option D
Explanation:
2t − 1 \(\leq\) 3 and 2 − t < 5
2t \(\leq\) 3 + 1 and 2 − 5 \(\leq\) t
2t \(\leq\) 4 and − 3 \(\leq\) t
t \(\leq\) 2 and − 3 \(\leq\) t or t \(\geq\) − 3
Combining the two ,starting from the last
-3 \(\leq\) t \(\leq\) 2
2t − 1 \(\leq\) 3 and 2 − t < 5
2t \(\leq\) 3 + 1 and 2 − 5 \(\leq\) t
2t \(\leq\) 4 and − 3 \(\leq\) t
t \(\leq\) 2 and − 3 \(\leq\) t or t \(\geq\) − 3
Combining the two ,starting from the last
-3 \(\leq\) t \(\leq\) 2