Question

1. which one of the following values satisfies the inequality \\(\frac{x}{-7} < 8\\)? \\(\bigcirc\\) \\(x = -69\\) a \\(\bigcirc\\) \\(x = -63\\) b \\(\bigcirc\\) \\(x = -49\\) c \\(\bigcirc\\) \\(x = -56\\) d

Explanation:

Step1: Solve the inequality for x

To solve \(\frac{x}{-7} < 8\), we multiply both sides by \(-7\). Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign flips. So we get:
\(x > 8\times(-7)\)
\(x > - 56\)

Step2: Check each option

• For option A (\(x = - 69\)): \(-69 < - 56\), so it does not satisfy \(x > - 56\).
• For option B (\(x=-63\)): \(-63 < - 56\), so it does not satisfy \(x > - 56\).
• For option C (\(x = - 49\)): \(-49 > - 56\), so it satisfies \(x > - 56\).
• For option D (\(x=-56\)): \(-56=-56\), and we need \(x > - 56\), so it does not satisfy.

Answer:

C. \(x = - 49\)