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Question
Marcus’s mom lets him play video games for a certain amount of time each day. He has already spent 9 minutes playing video games and has fewer than 27 minutes left to play. The inequality
t – 9 < 27 can be used to determine the number of minutes Marcus has left to play video games.
Which number line best represents the solution to the inequality?
Responses
A Image with alt text:
B Image with alt text:
C Image with alt text:
D Image with alt text:
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In order to determine the best representation of the solution to the inequality t - 9 < 27, we need to consider the values that satisfy the inequality.
If we add 9 to both sides of the inequality, we get t < 36. This means that any value of t that is less than 36 satisfies the inequality.
Therefore, the number line should start at 0 and go up to 36, but values greater than or equal to 36 should be excluded.
Out of the given options, the number line that best represents this solution is:
B) Image with alt text.
To solve the inequality t - 9 < 27, we need to find the possible values of t that satisfy the inequality.
First, we can add 9 to both sides of the inequality to isolate t: t - 9 + 9 < 27 + 9, which simplifies to t < 36.
Now, we need to represent this inequality on a number line.
The best number line representation for this inequality would be:
C) Image with alt text:
The number line should start at 0 and go up to 36, with an open circle at 36 to represent that it is not included in the solution. The shaded part of the number line should be to the left of 36, indicating that t is less than 36.
To determine the number of minutes Marcus has left to play video games, we need to solve the inequality t - 9 < 27. To do this, we need to isolate the variable t.
Begin by adding 9 to both sides of the inequality:
t - 9 + 9 < 27 + 9
This simplifies to:
t < 36
Now, we can represent the solution to the inequality on a number line. The variable t is less than 36, which means it can take any value less than 36 but not including 36.
The best representation of the solution on a number line would be option B, as it shows all the values less than 36 but not including 36.