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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 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 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 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.

1 answer

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

\[ x + 3 \leq 7 \] \[ x \leq 7 - 3 \] \[ x \leq 4 \]

The solution to this inequality is all values of \( x \) that are less than or equal to 4.

On a number line:

  • There should be a closed circle on 4 (indicating that 4 is included in the solution).
  • The line should extend to the left from 4 towards negative infinity, indicating all values less than 4 are included.

Based on the descriptions provided, the correct answer 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.