Question

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.
-20≤5x-5≤5


0
1
2
3
4
5
-1
-2
-3
-4
-5

Answer 1

To solve the compound inequality \(-20 \leq 5x - 5 \leq 5\), we can break it down into two parts.

**Step 1: Solve the left part of the inequality.**

\[
-20 \leq 5x - 5
\]

Add 5 to both sides:

\[
-20 + 5 \leq 5x
\]
\[
-15 \leq 5x
\]

Now, divide by 5:

\[
-3 \leq x
\]

This means \(x \geq -3\).

**Step 2: Solve the right part of the inequality.**

\[
5x - 5 \leq 5
\]

Add 5 to both sides:

\[
5x \leq 5 + 5
\]
\[
5x \leq 10
\]

Now, divide by 5:

\[
x \leq 2
\]

**Step 3: Combine the results.**

From the two parts, we have:

\[
-3 \leq x \leq 2
\]

**Step 4: Write the solution in interval notation.**

The solution in interval notation is:

\[
[-3, 2]
\]

**Step 5: Graph the solution on the number line.**

To graph the solution \([-3, 2]\):

- Draw a number line.
- Shade the area between -3 and 2.
- Use closed dots on -3 and 2 to indicate that these endpoints are included in the interval.

The graph will look like this:

```
<---|---|---|---|---|---|---|---|---|--->
-5 -4 -3 -2 -1 0 1 2 3 4
●================●
```

This indicates that the values of \(x\) in the interval \([-3, 2]\) satisfy the original inequality.