Question

Solve the following inequality for
x.


ax - 3 < 17

Answer 1

To solve the inequality \( ax - 3 < 17 \), we start by isolating \( x \).

1. Add 3 to both sides of the inequality:

\[
ax - 3 + 3 < 17 + 3
\]

which simplifies to:

\[
ax < 20
\]

2. 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.