Question

Solve the compound inequality and graph the solution.
-4x </ -28 or x/4 < 1

Answer 1

To solve the compound inequality \(-4x < -28\) or \(\frac{x}{4} < 1\), we will solve each part separately.

### Step 1: Solve \(-4x < -28\)

1. Divide both sides by -4. Remember that when you divide or multiply by a negative number, you must flip the inequality sign:
\[
x > 7
\]

### Step 2: Solve \(\frac{x}{4} < 1\)

1. Multiply both sides by 4:
\[
x < 4
\]

### Step 3: Combine the solutions

The solutions to the inequalities are:
1. \(x > 7\)
2. \(x < 4\)

Since it's an "or" compound inequality, the solution set is:
\[
x < 4 \quad \text{or} \quad x > 7
\]

### Step 4: Graph the solution

To graph this solution on a number line:
- For \(x < 4\), draw an open circle at 4 and shade to the left.
- For \(x > 7\), draw an open circle at 7 and shade to the right.

This can be represented visually as:

```
<---(----|----)--->
4 7
```

The shaded regions show that the solution includes all values less than 4 and greater than 7.