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Which of the following shows the graph of the solution to x+123>4

?(1 point)
Responses

A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked on the tick line above 5 and two thirds. A line is drawn from the circle 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. An open circle is marked on the tick line above 5 and two thirds. A line is drawn from the circle 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. An open circle is marked on the tick line above two and one third. A line is drawn from the circle 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. An open circle is marked on the tick line above two and one third. A line is drawn from the circle 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. An open circle is marked on the tick line above two and one third. A line is drawn from the circle 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. An open circle is marked on the tick line above two and one third. A line is drawn from the circle 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. An open circle is marked on the tick line above 5 and two thirds. A line is drawn from the circle toward negative 10 with an arrow at the end.

1 answer

To solve the inequality \( x + 123 > 4 \), we start by isolating \( x \).

  1. Subtract 123 from both sides: \[ x > 4 - 123 \] \[ x > -119 \]

This means that \( x \) can take on any value greater than \(-119\).

Now, when we represent this on a number line:

  • We will have an open circle at \(-119\) (indicating that -119 itself is not included in the solution).
  • The line will extend to the right of \(-119\), indicating all numbers greater than this value.

From your descriptions:

  • The first response marks an open circle at \( \frac{17}{3} \) (which is approximately \( 5.67 \)) and extends toward \( 10 \).
  • The second response marks an open circle at \( \frac{7}{3} \) (approximately \( 2.33 \)) and extends toward \( 10 \).
  • The third response marks an open circle at \( \frac{7}{3} \) and extends toward the left.
  • The fourth response marks an open circle at \( \frac{17}{3} \) and extends to the left.

None of the options correctly represent the solution \( x > -119 \). However, if we had the correct lower bound for these values, you would look for an open circle at the corresponding value greater than \(-119\) extending to the right.

It seems like none of the options provided depicts the graph of the solution \( x > -119 \). If you were looking for a value specifically like \(-119\), please double-check the options or provide the correct ones if available.