Which of the following is the correct solution to the inequality Cx+4≤18

, where C is a number greater than 0?(1 point)
Responses

Cx≤14
cap c x is less than or equal to 14 - no response given

x≤14
x is less than or equal to 14 - incorrect

C≤14x
cap c is less than or equal to 14 over x - no response given

x≤14C

1 answer

To solve the inequality \( Cx + 4 \leq 18 \), where \( C \) is a positive number, we start by isolating \( x \):

  1. Subtract 4 from both sides: \[ Cx \leq 18 - 4 \] \[ Cx \leq 14 \]

  2. Divide both sides by \( C \) (since \( C > 0 \), the direction of the inequality does not change): \[ x \leq \frac{14}{C} \]

From this, we can analyze the options given:

  • Cx ≤ 14: This is equivalent to our derived step before isolating \( x \), but does not complete the solution.
  • x ≤ 14: Incorrect.
  • C ≤ 14x: Not relevant here.
  • x ≤ 14C: Incorrect as it implies a different relationship.

The most directly correct answer is Cx ≤ 14.

However, the inequality implies that the relationship for \( x \) in terms of \( C \) implies \( x \leq \frac{14}{C} \), which was not provided in the multiple responses.

The correct context based on the original inequality is actually that once solved: \[ x \leq \frac{14}{C} \]

So, among the options clearly listed, the correct form that directly leads to identifying constraints on \( x \) would have been \( Cx \leq 14\), but for a conclusive numerically isolated inequality specifically for \( x \), \( x \leq \frac{14}{C} \) would have been ideal.

If \( C > 0 \), the inequality indicates that as \( C \) increases, the upper limit for \( x \) decreases.