Solve the following:

Question

ax + 15 = 44 _______________
ax - 44 < 15 _______________
Options: x = 29a, x < 59/a, x = 59a, x = 59/a, x = 29/a, x < 29a, x < 29/a, x> 59a

Answer 1

Let's solve each equation/inequality step by step.

1. For the equation \( ax + 15 = 44 \):

   We start by isolating \( ax \): \[ ax = 44 - 15 \] \[ ax = 29 \]

   Now, divide both sides by \( a \) (assuming \( a \neq 0 \)): \[ x = \frac{29}{a} \]

2. For the inequality \( ax - 44 < 15 \):

   We will also isolate \( ax \) here: \[ ax < 15 + 44 \] \[ ax < 59 \]

   Again, divide by \( a \) (assuming \( a > 0 \)): \[ x < \frac{59}{a} \]

   If \( a < 0 \), the direction of the inequality would change: \[ x > \frac{59}{a} \]

Summary of Results:

• The solution to the equation \( ax + 15 = 44 \) is: \[ x = \frac{29}{a} \]
• The solution to the inequality \( ax - 44 < 15 \) is: \[ x < \frac{59}{a} ; \text{if } a > 0 \text{ or } x > \frac{59}{a} ; \text{if } a < 0 \]

Matching to Options:

1. For \( ax + 15 = 44 \): The option that matches is: \[ x = \frac{29}{a} \]

2. For \( ax - 44 < 15 \) (assuming \( a > 0 \)): The option that matches is: \[ x < \frac{59}{a} \]

Thus, the final answers are:

• Equation: \( x = \frac{29}{a} \)
• Inequality: \( x < \frac{59}{a} \) (assuming \( a > 0 \))

Answer 2

are you sure these answer to the questions are correct

Answer 3

Let's double-check the calculations step-by-step to ensure accuracy.

1. For the equation:

   \[ ax + 15 = 44 \]

   To isolate \( ax \), we subtract 15 from both sides: \[ ax = 44 - 15 \] \[ ax = 29 \]

   Next, divide both sides by \( a \) (assuming \( a \neq 0 \)): \[ x = \frac{29}{a} \]

   This confirms that the solution is: \[ x = \frac{29}{a} \]

2. For the inequality:

   \[ ax - 44 < 15 \]

   We first add 44 to both sides: \[ ax < 15 + 44 \] \[ ax < 59 \]

   Now, we divide by \( a \). The direction of the inequality will depend on the sign of \( a \):

   • If \( a > 0 \), we divide by \( a \) without changing the inequality: \[ x < \frac{59}{a} \]
   • If \( a < 0 \), dividing by \( a \) reverses the inequality: \[ x > \frac{59}{a} \]

Summary:

• For the equation \( ax + 15 = 44 \):

  • The answer is \( x = \frac{29}{a} \).

• For the inequality \( ax - 44 < 15 \):

  • If \( a > 0 \): \( x < \frac{59}{a} \).
  • If \( a < 0 \): \( x > \frac{59}{a} \).

Conclusion:

Based on these calculations:

• The equation yields \( x = \frac{29}{a} \).
• The inequality leads to \( x < \frac{59}{a} \) if \( a > 0 \) or \( x > \frac{59}{a} \) if \( a < 0 \).

If you're limited to \( a > 0 \) for your selections, the final valid options for the equations would be:

Equation: \( x = \frac{29}{a} \)
Inequality: \( x < \frac{59}{a} \)

Both my previous response and this explanation confirm the correctness of these conclusions. If there are specific options you want me to match them against, please let me know!