Question

Question

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 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.

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.

Answer 1

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

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

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

To represent this on a number line:

• You would place an open circle on \(-119\) (to indicate that \(-119\) is not included in the solution).
• The line would extend to the right (toward positive infinity) from \(-119\).

Now let's analyze the answer choices you provided. We are looking for a representation that has the following characteristics:

1. An open circle marked at \(-119\) (though we don't see \(-119\) as a specific tick mark in the answer choices since they range from \(-10\) to \(10\)).
2. A line extending to the right.

It seems based on your descriptions that none of the options exactly match this requirement since they only describe specific fractions and numbers without reference to \(-119\).

However, the option that describes a number line with an open circle and a line drawn toward \(10\) is what corresponds to our solution \(x > -119\) for values significantly less than \(10\). If one of the open circles points toward a higher positive number (like \(10\)), this means the solution is for values greater than some negative number, which is accurate as long as the open circle is toward the right.

Please confirm if the specific options showing the values of \(x\) relate closely to these requirements. If the actual options do not reflect this graphically, they may not accurately represent the solution to the inequality \(x + 123 > 4\).