4. $$ 8-\frac{1}{4} n \geq 20 $$

Question

UpStudy AI · Accepted Answer

To solve the inequality:

$$
8 - \frac{1}{4}n \geq 20
$$

follow these steps:

### Step 1: Isolate the Term with $$ n $$

Subtract 8 from both sides to move the constant term to the right side of the inequality:

$$
8 - \frac{1}{4}n - 8 \geq 20 - 8
$$

Simplifying both sides:

$$
-\frac{1}{4}n \geq 12
$$

### Step 2: Solve for $$ n $$

To isolate $$ n $$, multiply both sides of the inequality by **-4**. **Important:** When you multiply or divide both sides of an inequality by a negative number, you must **reverse the inequality sign**.

$$
-\frac{1}{4}n \times (-4) \leq 12 \times (-4)
$$

Simplifying:

$$
n \leq -48
$$

### Conclusion

The solution to the inequality $$ 8 - \frac{1}{4}n \geq 20 $$ is:

$$
n \leq -48
$$

This means that any real number $$ n $$ that is **less than or equal to -48** satisfies the original inequality.
$$ n \leq -48 $$

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