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Answer :
To solve the problem, we need to find the possible values for [tex]\( f \)[/tex], which represents the length of the final song in seconds.
1. Set up the inequality:
We start with the inequality that represents the situation:
[tex]\( 190 > 60 + f \)[/tex].
2. Isolate [tex]\( f \)[/tex] in the inequality:
We want to solve for [tex]\( f \)[/tex]. To do this, we need to isolate [tex]\( f \)[/tex] on one side of the inequality:
[tex]\[
190 - 60 > f
\][/tex]
3. Simplify the inequality:
Calculate the left side:
[tex]\[
190 - 60 = 130
\][/tex]
So the inequality becomes:
[tex]\[
130 > f
\][/tex]
4. Determine the value and describe the number line:
This inequality means that [tex]\( f \)[/tex] must be less than 130 seconds. Therefore, on the number line, point [tex]\( f \)[/tex] should be any value less than 130, such as 129 or any smaller number.
5. Describe the appearance of the graph:
The graph of this inequality would be an open circle at 130 on the number line, with a line extending to the left, encompassing all values less than 130.
In conclusion:
- The value [tex]\( f \)[/tex] should be less than 130 seconds.
- On the number line, point [tex]\( f \)[/tex] can be marked at any number less than 130, such as at 70 as indicated in the problem statement.
These steps ensure that we understand how [tex]\( f \)[/tex] fits within the constraints provided by the original inequality.
1. Set up the inequality:
We start with the inequality that represents the situation:
[tex]\( 190 > 60 + f \)[/tex].
2. Isolate [tex]\( f \)[/tex] in the inequality:
We want to solve for [tex]\( f \)[/tex]. To do this, we need to isolate [tex]\( f \)[/tex] on one side of the inequality:
[tex]\[
190 - 60 > f
\][/tex]
3. Simplify the inequality:
Calculate the left side:
[tex]\[
190 - 60 = 130
\][/tex]
So the inequality becomes:
[tex]\[
130 > f
\][/tex]
4. Determine the value and describe the number line:
This inequality means that [tex]\( f \)[/tex] must be less than 130 seconds. Therefore, on the number line, point [tex]\( f \)[/tex] should be any value less than 130, such as 129 or any smaller number.
5. Describe the appearance of the graph:
The graph of this inequality would be an open circle at 130 on the number line, with a line extending to the left, encompassing all values less than 130.
In conclusion:
- The value [tex]\( f \)[/tex] should be less than 130 seconds.
- On the number line, point [tex]\( f \)[/tex] can be marked at any number less than 130, such as at 70 as indicated in the problem statement.
These steps ensure that we understand how [tex]\( f \)[/tex] fits within the constraints provided by the original inequality.
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