Relationships Between Quantities — Test

Question 23 • Algebra II

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 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 going in the opposite direction.

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 going in the opposite direction.

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 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

Start with |2x − 6| < 4, which means −4 < 2x − 6 < 4. Add 6 throughout and divide by 2 to get 1 < x < 5. The solution includes all numbers between 1 and 5, but not the endpoints, so the correct number line has open circles at 1 and 5 connected: choice C.

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