Solve the following for a: ax−5>18

Answer 1

To solve the inequality \( ax - 5 > 18 \) for \( a \), follow these steps:

1. Start by isolating the term involving \( a \):

   \[ ax - 5 > 18 \]

2. Add 5 to both sides:

   \[ ax > 23 \]

3. Now, divide both sides by \( x \) (assuming \( x \neq 0 \)) to solve for \( a \):

   \[ a > \frac{23}{x} \]

Thus, the solution for \( a \) in terms of \( x \) is:

\[ a > \frac{23}{x} \]

Keep in mind that the solution is valid for \( x \neq 0 \). Also, depending on the sign of \( x \), you may need to reverse the inequality sign when dividing:

• If \( x > 0 \), then \( a > \frac{23}{x} \).
• If \( x < 0 \), then \( a < \frac{23}{x} \).

If \( x = 0 \), the original inequality \( ax - 5 > 18 \) cannot be evaluated as it leads to an expression involving division by zero.

Answer 2

A. a > 23x

B. a = 23+x

C. a = 23x

D. a > 13x

Answer 3

Let's revisit the inequality \( ax - 5 > 18 \) and solve it step by step.

1. We start with the original inequality: \[ ax - 5 > 18 \]

2. Add 5 to both sides to isolate the term containing \( a \): \[ ax > 23 \]

3. Now, divide both sides by \( x \) (assuming \( x \neq 0 \)): \[ a > \frac{23}{x} \]

From here, we need to see which choice corresponds to our result \( a > \frac{23}{x} \).

Given the options:

• A. \( a > 23x \)
• B. \( a = 23 + x \)
• C. \( a = 23x \)
• D. \( a > 13x \)

None of these options exactly match our derived result \( a > \frac{23}{x} \). However:

• If \( x > 0 \), \( \frac{23}{x} \) is greater than \( 13x \) for sufficiently small values of \( x \).
• If \( x < 0 \), \( \frac{23}{x} < 0\) could effect the inequality based on the sign of \( x \).

Therefore, we cannot definitively choose from the provided options without knowing the sign of \( x \), but \( a > 23x\) (A) could hold true for negative \( x \) values (as increasing the divisor decreases the whole ratio). If we consider that all choices must hold for \( x \ne 0 \) and find out that \( x\) could take both positive and negative values, none of those options sublimate \( a > \frac{23}{x} \) directly.

If we were to pick an answer and take into consideration the necessity for general solutions in a broad context recognizing conditions of x-values, option A seems closer primarily supporting the definition provided, otherwise effectiveness would rely on \( x\) being clearly defined.