Question

Solve the following inequality for
x.
y is less than or equal to -ax + 5

Answer 1

To solve the inequality \( y \leq -ax + 5 \) for \( x \), follow these steps:

1. **Isolate the term containing \( x \)**:
\[
y - 5 \leq -ax
\]

2. **Divide by \(-a\)** (remember to reverse the inequality sign if \( a > 0 \)):
\[
\frac{y - 5}{-a} \geq x \quad \text{if } a > 0
\]
or
\[
\frac{y - 5}{-a} \leq x \quad \text{if } a < 0
\]

3. **Rearranging gives**:
- If \( a > 0 \):
\[
x \leq \frac{5 - y}{a}
\]
- If \( a < 0 \):
\[
x \geq \frac{5 - y}{a}
\]

In summary, the solution for \( x \) depends on the sign of \( a \):
- If \( a > 0 \): \( x \leq \frac{5 - y}{a} \)
- If \( a < 0 \): \( x \geq \frac{5 - y}{a} \)

Make sure to note the case when \( a = 0 \), when the inequality becomes undefined for \( x \).