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

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.

GPT-4o mini · Answer

To solve the inequality $ x + 3 \leq 7 $, we first isolate $ x $: $$ x + 3 \leq 7 $$ $$ x \leq 7 - 3 $$ $$ x \leq 4 $$ This means that $ x $ can take any value less than or equal to 4. On a number line, we represent this by: - A closed circle at 4 (to indicate that 4 is included in the solution). - A line extending from 4 to the left to show all values less than 4, with an arrow at the left end indicating it goes to negative infinity. Considering the options you provided, the correct graph for the solution $ x \leq 4 $ 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 describes the right graph for $ x + 3 \leq 7 $.