Question

HELP NEEDED URGENT

Which graph represents the solutions to the inequality |2x − 6| < 4? 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

Answer: The correct option is (D) number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.

Step-by-step explanation: We are given to select the correct graph from the options that will represent the solution to the following inequality.

`|2x-6|<4.`

To draw the graph of the above inequality, first we have to solve the inequality.

The solution is as follows:

`|2x-6|<4\\\\\Rightarrow 2x-6<4~~\textup{or}~~-(2x-6)<4\\\\ \Rightarrow 2x<10~~~~~~~~~~~\Rightarrow 2x-6>-4\\\\\Rightarrow x<5~~~~~~~~~~~~~~\Rightarrow 2x>2\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~\Rightarrow x>1.`

Therefore, the solution is x > 1, x < 5.

Thus, the solution of the inequality is given by

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

The solution on the number line is shown in the attached figure.

Option (D) is correct.