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

?(1 point)
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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.
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 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 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 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.

1 answer

To solve the inequality \( x + 123 > 4 \), you first isolate \( x \):

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

This means the solution includes all values greater than -119.

Now, let's analyze the descriptions of the graphs provided:

  • First option: Open circle at \( \frac{17}{3} \) (which is approximately 5.67), pointing left (representing values less than \( \frac{17}{3} \)).
  • Second option: Open circle at \( \frac{7}{3} \) (approximately 2.33), pointing left.
  • Third option: Open circle at \( \frac{17}{3} \) (approximately 5.67), pointing right (representing values greater than \( \frac{17}{3} \)).
  • Fourth option: Open circle at \( \frac{7}{3} \) (approximately 2.33), pointing right.

Since the solution is \( x > -119 \), we are looking for a graph that has an open circle and an arrow pointing to the right. Both the third and fourth options point to the right, but we need to check the open circle placement:

  • The third option's open circle is at \( 5 \frac{2}{3} \) (or \( \frac{17}{3} \)), which is above -119.
  • The fourth option's open circle is at \( 2 \frac{1}{3} \) (or \( \frac{7}{3} \)), also above -119.

However, since both represent values greater than the respective open circle, the correct graph that shows all values greater than \( -119 \) should ideally have an open circle placed lower than \( -119 \).

The graph that best represents our solution would be:

Third option: A number line with an open circle above \( \frac{17}{3} \) (meaning values greater than \( 5 \frac{2}{3} \)) and an arrow pointing towards 10.

Hence the answer is: The third option.