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Solve the equation and inequality for x, assuming a > 0.(2 points)

Put responses in the correct input to answer the question.
a) ax+15=44
Solution: Response area

b) ax−44<15
Solution:

1 answer

Let's solve each part step by step.

a) Solve the equation \( ax + 15 = 44 \).

  1. Subtract 15 from both sides of the equation: \[ ax = 44 - 15 \] \[ ax = 29 \]
  2. Now, divide both sides by \( a \) (since \( a > 0 \)): \[ x = \frac{29}{a} \]

Solution (for a): \( x = \frac{29}{a} \)

b) Solve the inequality \( ax - 44 < 15 \).

  1. Add 44 to both sides of the inequality: \[ ax < 15 + 44 \] \[ ax < 59 \]
  2. Now, divide both sides by \( a \) (since \( a > 0 \), the inequality sign remains the same): \[ x < \frac{59}{a} \]

Solution (for b): \( x < \frac{59}{a} \)

Final Answers

a) Solution: \( \frac{29}{a} \)

b) Solution: \( x < \frac{59}{a} \)