Question

solve and gragh the linear inequality
-10<2+x<-1

Answer 1

To solve the linear inequality \(-10 < 2 + x < -1\), we will break it down into two parts:

1. Solve the left inequality: \(-10 < 2 + x\)
2. Solve the right inequality: \(2 + x < -1\)

### Step 1: Solve \(-10 < 2 + x\)

Subtract 2 from both sides:

\[
-10 - 2 < x
\]
\[
-12 < x
\]
This can be rewritten as:
\[
x > -12
\]

### Step 2: Solve \(2 + x < -1\)

Subtract 2 from both sides:

\[
x < -1 - 2
\]
\[
x < -3
\]

### Combining the Inequalities

Now we combine the two results:

\[
-12 < x < -3
\]

### Graphing the Inequality

To graph this compound inequality on a number line:

- Draw a number line.
- Mark the points \(-12\) and \(-3\).
- Use an open circle (or parentheses) at \(-12\) and \(-3\) to indicate that these points are not included in the solution.
- Shade the region between \(-12\) and \(-3\).

### Final Result

The solution to the inequality is:
\[
-12 < x < -3
\]

The graph can be represented visually with an open interval between \(-12\) and \(-3\) on the number line. Here is an approximate sketch of the number line:

```
-------o=================o-------
-12 -3
```
This indicates that \(x\) can take any value between \(-12\) and \(-3\), but not including these endpoints.

Answer 2

give me a simmiliar question

Answer 3

Sure! Here’s a similar linear inequality for you to solve:

\[
-5 < 3 + y < 4
\]

You can follow the same steps as before to solve this inequality and graph the result. If you need help with it, feel free to ask!

Answer 4

is this right -5<3+y<4
Subtract 3 from all sides
-8<y<1

Answer 5

Yes, that’s correct! Let’s go through the steps together to make sure everything is clear:

Given the inequality:

\[
-5 < 3 + y < 4
\]

### Step 1: Split into Two Inequalities

You correctly interpreted this as two inequalities:

1. \(-5 < 3 + y\)
2. \(3 + y < 4\)

### Step 2: Solve Each Inequality

#### Solve \(-5 < 3 + y\)

Subtract 3 from both sides:

\[
-5 - 3 < y
\]
\[
-8 < y
\]

Which can also be written as:

\[
y > -8
\]

#### Solve \(3 + y < 4\)

Subtract 3 from both sides:

\[
y < 4 - 3
\]
\[
y < 1
\]

### Step 3: Combine the Results

Putting the two results together, we get:

\[
-8 < y < 1
\]

### Conclusion

So, your solution of:

\[
-8 < y < 1
\]

is indeed correct! Great job! If you need further assistance or have any more questions, feel free to ask.