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

Question

?(1 point)
Responses

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.
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 13 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.

Answer 1

To solve the inequality \( x + 3 \leq 7 \), we first isolate \( x \):

\[ x + 3 \leq 7 \]

Subtract 3 from both sides:

\[ x \leq 7 - 3 \]

This simplifies to:

\[ x \leq 4 \]

Now, we need to represent this on a number line. The solution \( x \leq 4 \) means that \( x \) can take any value less than or equal to 4.

On the number line:

• There will be a closed circle at 4 (indicating that 4 is included in the solution).
• A line will extend to the left of 4 (indicating all values less than 4), toward negative infinity.

Looking at the provided options, the correct graph representation of the solution \( x \leq 4 \) should reflect these points.

The correct option is:

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 option shows that the solution includes all numbers less than or equal to 4.