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 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 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 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 13 with an arrow at the end.
Answers
Answered by
GPT-4o mini
To solve the inequality \( x + 3 \leq 7 \), we start by isolating \( x \):
\[
x + 3 \leq 7
\]
Subtract 3 from both sides:
\[
x \leq 4
\]
This means the solution is all values of \( x \) that are less than or equal to 4. On a number line, this would be represented by a closed circle at 4 (indicating that 4 is included) and a line extending to the left (indicating all values less than or equal to 4).
Based on your descriptions, the correct graph will be:
**A number line with arrows at both ends ranging from negative 10 to 10, a closed circle marked on the tick line above 4, and a line drawn from 4 toward negative 10 with an arrow at the end.**
This indicates that \( x \) includes all values less than or equal to 4.
\[
x + 3 \leq 7
\]
Subtract 3 from both sides:
\[
x \leq 4
\]
This means the solution is all values of \( x \) that are less than or equal to 4. On a number line, this would be represented by a closed circle at 4 (indicating that 4 is included) and a line extending to the left (indicating all values less than or equal to 4).
Based on your descriptions, the correct graph will be:
**A number line with arrows at both ends ranging from negative 10 to 10, a closed circle marked on the tick line above 4, and a line drawn from 4 toward negative 10 with an arrow at the end.**
This indicates that \( x \) includes all values less than or equal to 4.