Which of the following shows the graph of the solution to x+1 2/34 ?(1 point) Responses 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. 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. 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.

Question

Which of the following shows the graph of the solution to x+1 2/3>4 ?(1 point) Responses 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. 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. 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.

GPT-4o mini · Answer

To solve the inequality $ x + \frac{1}{3} > 4 $, we first isolate $ x $: 1. Subtract $ \frac{1}{3} $ from both sides: $$ x > 4 - \frac{1}{3} $$ 2. Convert 4 to a fraction: $$ 4 = \frac{12}{3} $$ 3. Now, perform the subtraction: $$ x > \frac{12}{3} - \frac{1}{3} = \frac{11}{3} $$ Next, convert $ \frac{11}{3} $ into a mixed number: $$ \frac{11}{3} = 3\frac{2}{3} \approx 3.67 $$ The solution to the inequality is $ x > \frac{11}{3} $ or $ x > 3.67 $. On a number line, this would be indicated by an open circle at $ \frac{11}{3} $ (which is approximately $ 3.67 $, or $ 3\frac{2}{3} $) and a line extending to the right towards positive infinity. Based on this analysis, you should look for the graph that has: - An open circle at $ \frac{11}{3} $ (or around 3.67). - A line drawn to the right towards positive infinity. If none of the responses directly mention $ \frac{11}{3} $, remember it is also equal to $ 3.67 $, so find the depiction closest to that value going towards positive infinity.