Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Solve for x: |2x + 6| − 4 = 20

Sagot :

The answers are in the attachment below. x=9, and x=-15.
View image Аноним
Morganlovescats

The area between the two bars is the absolute value, or how far the value is from 0 on the number line.

To solve this problem, first, you have to isolate the absolute value on one side of the equation. From there, you have two "branches" of the problem. One includes the "positive" version of the equation, the other is the "negative" version.

To isolate the absolute value:

|2x + 6| - 4 = 20

|2x + 6| = 24

Then, you need to complete each "branch" of the problem. For the positive one:

2x + 6 = 24

2x = 18

x = 9

After you find x, you need to check for extraneous solutions, or solutions that do not work in the problem. To do this, plug x in to the original equation:

|2(9) + 6| - 4 = 20

|18 + 6| - 4 = 20

|24| - 4 = 20

24 - 4 = 20

20 = 20

So the statement x = 9 works for this equation. Now you have to work on the negative branch.

2x + 6 = -24

2x = -30

x = -15

Check for extraneous solutions:

|2(-15) + 6| - 4 = 20

|-30 + 6| - 4 = 20

|-24| - 4 = 20

24 - 4 = 20

20 = 20

In conclusion, x has two values: x = 9 and x = -15.

Hope I helped!! :)

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.