Question

Solve the following:(2 points)

ax−44<15
ax+15=44

Answer 1

To solve the given inequalities and equation, we need to isolate the variable \(x\) in each case.

1. **Inequality**: \(ax - 44 < 15\)

First, add 44 to both sides:
\[
ax < 15 + 44
\]
\[
ax < 59
\]

Now, divide both sides by \(a\) (assume \(a \neq 0\)):
\[
x < \frac{59}{a} \quad \text{if } a > 0
\]
or
\[
x > \frac{59}{a} \quad \text{if } a < 0
\]

2. **Equation**: \(ax + 15 = 44\)

Subtract 15 from both sides:
\[
ax = 44 - 15
\]
\[
ax = 29
\]

Now, divide both sides by \(a\) (again assuming \(a \neq 0\)):
\[
x = \frac{29}{a}
\]

### Summary:
- For the inequality \(ax - 44 < 15\):
- If \(a > 0\), \(x < \frac{59}{a}\)
- If \(a < 0\), \(x > \frac{59}{a}\)

- For the equation \(ax + 15 = 44\):
- \(x = \frac{29}{a}\)

Let me know if you need further assistance!