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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 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 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.
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 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.

1 answer

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

  1. Subtract 3 from both sides: \[ x \leq 7 - 3 \] \[ x \leq 4 \]

Now we have the solution \(x \leq 4\). This means that \(x\) can take any value less than or equal to 4.

In a number line representation:

  • We should have a closed circle on 4, indicating that 4 is included in the solution.
  • The line should extend to the left of 4, indicating all values less than 4.

Looking at the responses provided:

  • The correct representation would be one that shows a closed circle above 4 and a line extending to the left towards negative numbers.

Based on the descriptions you provided, the third option matches this criteria:

"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 shows \(x \leq 4\) correctly.