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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 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 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.
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1 answer

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

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

This means \(x\) can take any value greater than \(-119\). In terms of a graph on a number line, this is represented by:

  • An open circle at \(-119\), indicating that \(-119\) itself is not included in the solution.
  • A solid line (or arrow) extending to the right, indicating that all numbers greater than \(-119\) are included in the solution.

Among the responses provided, evaluate which number line represents this scenario.

Since \(-119\) is not listed among the tick marks in the provided options, we have to look for the closest representation for \(x > -119\).

From the options:

  • The first response shows an open circle above \(5 \frac{2}{3}\) and extends to \(10\), which does not correspond to our solution.
  • The second response also shows an open circle at \(5 \frac{2}{3}\) but extends towards negative infinity, which is not correct either.
  • The third response has an open circle at \(2 \frac{1}{3}\) and extends towards negative infinity, which does not match our inequality either.
  • The fourth response shows an open circle at \(2 \frac{1}{3}\) and extends towards \(10\), which also is not aligned with our inequality.

None of the responses feature an open circle at \(-119\) or an extension to the right in accordance with \(x > -119\).

Therefore, if strictly confined to the options given, none perfectly reflect the graph of the solution to the inequality. You may need to check if there's a misunderstanding or clarification needed regarding the value marked on the number line. If a correct representation is not among the options, the test may require a different response approach.