Solve the inequality: -7 \(\leq\) 9 - 8x < 16 - x
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Correct Answer: Option D
Explanation:
-7 \(\leq\) 9 - 8x < 16 - x
-7 \(\leq\) 9 - 8x and 9 - 8x < 16 - x
-7 - 9 \(\leq\) -8x and -8x + x < 16 - 9
-16 \(\leq\) -8x and -7x < 7
\(\therefore\) x \(\leq\) 2 and -1 < x
-1 < x \(\leq\) 2.
-7 \(\leq\) 9 - 8x < 16 - x
-7 \(\leq\) 9 - 8x and 9 - 8x < 16 - x
-7 - 9 \(\leq\) -8x and -8x + x < 16 - 9
-16 \(\leq\) -8x and -7x < 7
\(\therefore\) x \(\leq\) 2 and -1 < x
-1 < x \(\leq\) 2.