To solve the inequality \( ax - 3 < 17 \), we start by isolating \( x \).
- Add 3 to both sides of the inequality:
\[ ax - 3 + 3 < 17 + 3 \]
which simplifies to:
\[ ax < 20 \]
- Next, divide both sides by \( a \). However, we must consider the sign of \( a \) because this affects the direction of the inequality:
- If \( a > 0 \):
\[ x < \frac{20}{a} \]
- If \( a < 0 \):
\[ x > \frac{20}{a} \]
- If \( a = 0 \):
The inequality \( ax - 3 < 17 \) becomes \(-3 < 17\), which is always true, meaning any value of \( x \) is a solution.
So the solution set is:
- For \( a > 0 \): \( x < \frac{20}{a} \)
- For \( a < 0 \): \( x > \frac{20}{a} \)
- For \( a = 0 \): \( x \) can be any real number.