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Answer :
To solve the problem, we need to interpret the inequality and determine the correct placement of point [tex]\( f \)[/tex] on the number line, as well as describe how the graph looks.
### Step-by-Step Solution
1. Understanding the Inequality:
- We start with the inequality [tex]\( 190 > 60 + f \)[/tex].
- Here, [tex]\( 190 \)[/tex] represents the length of the first song, and [tex]\( 60 + f \)[/tex] represents a value more than the length of the final song.
- Our goal is to find out what [tex]\( f \)[/tex] (the length of the final song) could be.
2. Solving the Inequality:
- We rearrange the inequality to solve for [tex]\( f \)[/tex]:
[tex]\[
190 > 60 + f
\][/tex]
- Subtract 60 from both sides to isolate [tex]\( f \)[/tex]:
[tex]\[
190 - 60 > f
\][/tex]
- Simplify this to:
[tex]\[
130 > f
\][/tex]
- This tells us that [tex]\( f \)[/tex] must be less than 130 seconds.
3. Identifying the Point on the Number Line:
- Since [tex]\( f \)[/tex] must be less than 130, a suitable point on the number line could be any value less than 130. For simplicity, let's choose 129 seconds, which satisfies the inequality.
4. Describing the Graph:
- The graph representing this inequality [tex]\( f < 130 \)[/tex] will have an open circle at 130 on the number line to indicate that 130 is not included.
- The arrow extends to the left from 130, showing that all values less than 130 are part of the solution.
### Conclusion
- Which value should point [tex]\( f \)[/tex] on the number line be?: 129
- Which best describes the appearance of the graph?: The graph is open at 130 and extends to the left.
### Step-by-Step Solution
1. Understanding the Inequality:
- We start with the inequality [tex]\( 190 > 60 + f \)[/tex].
- Here, [tex]\( 190 \)[/tex] represents the length of the first song, and [tex]\( 60 + f \)[/tex] represents a value more than the length of the final song.
- Our goal is to find out what [tex]\( f \)[/tex] (the length of the final song) could be.
2. Solving the Inequality:
- We rearrange the inequality to solve for [tex]\( f \)[/tex]:
[tex]\[
190 > 60 + f
\][/tex]
- Subtract 60 from both sides to isolate [tex]\( f \)[/tex]:
[tex]\[
190 - 60 > f
\][/tex]
- Simplify this to:
[tex]\[
130 > f
\][/tex]
- This tells us that [tex]\( f \)[/tex] must be less than 130 seconds.
3. Identifying the Point on the Number Line:
- Since [tex]\( f \)[/tex] must be less than 130, a suitable point on the number line could be any value less than 130. For simplicity, let's choose 129 seconds, which satisfies the inequality.
4. Describing the Graph:
- The graph representing this inequality [tex]\( f < 130 \)[/tex] will have an open circle at 130 on the number line to indicate that 130 is not included.
- The arrow extends to the left from 130, showing that all values less than 130 are part of the solution.
### Conclusion
- Which value should point [tex]\( f \)[/tex] on the number line be?: 129
- Which best describes the appearance of the graph?: The graph is open at 130 and extends to the left.
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