Mathematical Modeling — Test

Question 7 • Algebra 2 with Probability

Edmundo used a number line to show the solution for the inequality start absolute value 2 x minus 6 end absolute value is less than 4 Which number line shows the solution?

Answer

Image with description A horizontal number line shows two separate intervals. One interval begins with an open circle at negative 5 and extends indefinitely to the left. The other interval begins with an open circle at negative 1 and extends indefinitely to the right. Arrowheads indicate both rays continue beyond the number line.

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Open circles are on 1 and 5 and are connected.

Image with description A horizontal number line shows two separate intervals. One interval begins with an open circle at 1 and extends indefinitely to the left. The other interval begins with an open circle at 5 and extends indefinitely to the right. Arrowheads indicate both rays continue beyond the number line.

Image with description A number line marked as x ranges from negative 6 to 6 in intervals of 1. Open circles are on negative 5 and negative 1 and are connected.

Explanation

Solve the absolute value inequality by writing it as a compound inequality: −4 < 2x − 6 < 4. Add 6 throughout and divide by 2 to get 1 < x < 5. The solution is the interval between 1 and 5, with open circles at both endpoints, so the correct choice is the number line connecting 1 and 5.

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