To solve the inequality [tex]\( 5 \leq 2u - 1 < 17 \)[/tex], we need to break it into two parts and solve each part step-by-step.
### Step 1: Solve the left part of the inequality
We start with:
[tex]\[ 5 \leq 2u - 1 \][/tex]
1. Add 1 to both sides of the inequality:
[tex]\[ 5 + 1 \leq 2u - 1 + 1 \][/tex]
[tex]\[ 6 \leq 2u \][/tex]
2. Divide both sides by 2 to isolate [tex]\( u \)[/tex]:
[tex]\[ \frac{6}{2} \leq \frac{2u}{2} \][/tex]
[tex]\[ 3 \leq u \][/tex]
So the solution to the left part is:
[tex]\[ u \geq 3 \][/tex]
### Step 2: Solve the right part of the inequality
We next take:
[tex]\[ 2u - 1 < 17 \][/tex]
1. Add 1 to both sides of the inequality:
[tex]\[ 2u - 1 + 1 < 17 + 1 \][/tex]
[tex]\[ 2u < 18 \][/tex]
2. Divide both sides by 2 to isolate [tex]\( u \)[/tex]:
[tex]\[ \frac{2u}{2} < \frac{18}{2} \][/tex]
[tex]\[ u < 9 \][/tex]
So the solution to the right part is:
[tex]\[ u < 9 \][/tex]
### Step 3: Combine the results
We need [tex]\( u \)[/tex] to satisfy both parts of the inequality simultaneously. Thus, combining the results from the two steps, we have:
[tex]\[ 3 \leq u < 9 \][/tex]
### Conclusion
The solution to the inequality [tex]\( 5 \leq 2u - 1 < 17 \)[/tex] is:
[tex]\[ 3 \leq u < 9 \][/tex]
