Question

determine which of the following values of x satisfy the inequality below.
\\(\frac{x}{5} + 4 < -7\\)

a) -40

b) -55

c) -70

correct answer

c) -70

Explanation:

Step1: Solve the inequality for x

To solve \(\frac{x}{5}+4 < -7\), first subtract 4 from both sides:
\(\frac{x}{5}+4 - 4< -7 - 4\)
\(\frac{x}{5}< -11\)
Then multiply both sides by 5:
\(x < - 11\times5\)
\(x < - 55\)

Step2: Check each option

• Option A: \(x=-40\), since \(-40>-55\), it does not satisfy \(x < - 55\).
• Option B: \(x = - 55\), since \(-55\) is not less than \(-55\) (it is equal), it does not satisfy \(x < - 55\).
• Option C: \(x=-70\), since \(-70 < - 55\), it satisfies the inequality.

Answer:

C) -70