Question

Solve for u.
3≤u+9<4
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 3 \leq u + 9 < 4 \), we can break it into two separate inequalities:

1. \( 3 \leq u + 9 \)
2. \( u + 9 < 4 \)

Let's solve each part step by step.

### Step 1: Solve \( 3 \leq u + 9 \)
Subtract 9 from both sides:

\[
3 - 9 \leq u
\]

\[
-6 \leq u
\]

This can also be written as:

\[
u \geq -6
\]

### Step 2: Solve \( u + 9 < 4 \)
Subtract 9 from both sides:

\[
u < 4 - 9
\]

\[
u < -5
\]

### Step 3: Combine the results
Now we can combine the results from the two parts:

\[
-6 \leq u < -5
\]

### Final Answer
The solution for \( u \) as a compound inequality with integers is:

\[
-6 \leq u < -5
\]

This means that \( u \) can take the value of -6, but it cannot go above -5.