To find the range of users that access the website each day, we need to solve the inequality [tex]\( |125 - u| \leq 30 \)[/tex].
The absolute value inequality [tex]\( |125 - u| \leq 30 \)[/tex] can be split into two separate inequalities:
1. [tex]\( 125 - u \leq 30 \)[/tex]
2. [tex]\( 125 - u \geq -30 \)[/tex]
Let's solve each inequality separately.
### Solving the first inequality: [tex]\( 125 - u \leq 30 \)[/tex]
1. Subtract 125 from both sides:
[tex]\[
-u \leq 30 - 125
\][/tex]
2. Simplify the right side:
[tex]\[
-u \leq -95
\][/tex]
3. Multiply both sides by -1 (note that this reverses the inequality):
[tex]\[
u \geq 95
\][/tex]
### Solving the second inequality: [tex]\( 125 - u \geq -30 \)[/tex]
1. Subtract 125 from both sides:
[tex]\[
-u \geq -30 - 125
\][/tex]
2. Simplify the right side:
[tex]\[
-u \geq -155
\][/tex]
3. Multiply both sides by -1 (again, this reverses the inequality):
[tex]\[
u \leq 155
\][/tex]
### Combining both inequalities:
Putting these together, we have:
[tex]\[
95 \leq u \leq 155
\][/tex]
So, the range of users [tex]\( u \)[/tex] that access the website each day is represented by the interval [tex]\( 95 \leq u \leq 155 \)[/tex].
Therefore, the correct answer is:
[tex]\[ 95 \leq u \leq 155 \][/tex]
