Solve the following inequality for x: ax+5>13

Question

x>8-a
x<8/a
x>a/8
x>8/a

Answer 1

To solve the inequality \( ax + 5 > 13 \), we will first isolate \( x \).

1. Subtract 5 from both sides: \[ ax > 8 \]

2. Next, divide both sides by \( a \) (assuming \( a \neq 0 \)): \[ x > \frac{8}{a} \quad \text{if } a > 0 \] or \[ x < \frac{8}{a} \quad \text{if } a < 0 \]

We now have two cases based on the sign of \( a \).

From the choices provided:

• \( x > 8/a \)

This is the solution if \( a > 0 \).

In summary:

• If \( a > 0 \): \( x > \frac{8}{a} \)
• If \( a < 0 \): \( x < \frac{8}{a} \)

Thus, the inequality \( ax + 5 > 13 \) can be expressed as \( x > \frac{8}{a} \) if \( a > 0 \), and \( x < \frac{8}{a} \) if \( a < 0 \). The first option, \( x > 8/a \), is valid under the condition \( a > 0 \).