Question
Which of the following shows the graph of the solution to x+3≤7
?(1 point)
Responses
A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.
A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward negative 7 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward negative 7 with an arrow at the end.
A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward 10 with an arrow at the end.
A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward 13 with an arrow at the end.
?(1 point)
Responses
A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward negative 10 with an arrow at the end.
A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward negative 7 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward negative 7 with an arrow at the end.
A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. A closed circle is marked on the tick line above 4. A line is drawn from 4 toward 10 with an arrow at the end.
A number line with arrows at both the ends ranges from negative 7 to 13 in unit increments. A closed circle is marked on the tick line above 10. A line is drawn from 10 toward 13 with an arrow at the end.
Answers
Answered by
GPT-4o mini
To solve the inequality \( x + 3 \leq 7 \), we first isolate \( x \):
\[
x \leq 7 - 3
\]
\[
x \leq 4
\]
This means that the solution includes all values of \( x \) that are less than or equal to 4.
On a number line, this would be represented as:
- A closed circle at 4 (indicating that 4 is included in the solution).
- A line extending to the left (towards negative infinity) from 4, indicating all numbers less than 4 are included in the solution.
Given these characteristics, the correct graph of the solution to the inequality \( x + 3 \leq 7 \) is:
1. A number line ranging from negative 10 to 10.
2. A closed circle marked at 4.
3. A line extending from 4 toward negative 10 with an arrow at the end.
Therefore, the first option describes the correct representation of \( x + 3 \leq 7 \).
\[
x \leq 7 - 3
\]
\[
x \leq 4
\]
This means that the solution includes all values of \( x \) that are less than or equal to 4.
On a number line, this would be represented as:
- A closed circle at 4 (indicating that 4 is included in the solution).
- A line extending to the left (towards negative infinity) from 4, indicating all numbers less than 4 are included in the solution.
Given these characteristics, the correct graph of the solution to the inequality \( x + 3 \leq 7 \) is:
1. A number line ranging from negative 10 to 10.
2. A closed circle marked at 4.
3. A line extending from 4 toward negative 10 with an arrow at the end.
Therefore, the first option describes the correct representation of \( x + 3 \leq 7 \).