Question

Solve the following inequality for x.
ax - 3 < 17

Answer 1

To solve the inequality \( ax - 3 < 17 \), follow these steps:

1. Add 3 to both sides of the inequality:
\[
ax < 17 + 3
\]
\[
ax < 20
\]

2. Now, divide both sides by \( a \). Note that the direction of the inequality will change if \( a < 0 \):
- If \( a > 0 \):
\[
x < \frac{20}{a}
\]
- If \( a < 0 \):
\[
x > \frac{20}{a}
\]
- If \( a = 0 \), the inequality \( -3 < 17 \) is always true, meaning \( x \) can be any real number.

So, the solution to the inequality depends on the value of \( a \):

- If \( a > 0 \):
\[
x < \frac{20}{a}
\]

- If \( a < 0 \):
\[
x > \frac{20}{a}
\]

- If \( a = 0 \):
\[
x \text{ is any real number.}
\]