On any given day, the number of users, [tex]u[/tex], that access a certain website can be represented by the inequality [tex]|125 - u| \leq 30[/tex]. Which of the following represents the range of users that access the website each day?
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]
