Which of the following shows the graph of the solution to x+3≤7

Question

𝑥
+
3
≤
7
?(1 point)
Responses

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.

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.

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.

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 fr..............................

Answer 1

To solve the inequality \( x + 3 \leq 7 \), we first isolate \( x \) by subtracting \( 3 \) from both sides:

\[ x + 3 - 3 \leq 7 - 3 \]

This simplifies to:

\[ x \leq 4 \]

The solution to this inequality indicates that \( x \) can take on any value less than or equal to \( 4 \).

On a number line, this would be represented with a closed circle on \( 4 \) (indicating that \( 4 \) is included in the solution) and a line extending to the left (toward negative infinity), indicating all values less than \( 4 \).

Based on the descriptions provided, the correct response is:

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.

This image accurately represents the solution \( x \leq 4 \).