Question

Which graph represents the solutions to the inequality |2x − 6| < 4? (5 points) number line with a closed circle on 1, shading to the left and a closed circle on 5, shading to the right number line with a closed circle on 1, shading to the right and a closed circle on 5, shading to the left number line with an open circle on 1, shading to the left and an open circle on 5, shading to the right number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left

Answer 1

The graph that represents the inequality is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

What is the inequality?

The inequality is:

|2x - 6| < 4

Which means that the distance of 2x - 6 to the origin is less than 4, hence:

-4 < 2x - 6 < 4.

The solution is:

2x - 6 > -4

2x > 2

x > 1

2x - 6 < 4

2x < 10

x < 5

The solution has open circles at x = 1 and x = 5, as they are not part of the solution, and the shading is in the middle, as the solution is 1 < x < 5, hence the correct option is:

Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

More can be learned about inequalities at https://brainly.com/question/25235995

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