Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our 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!! :)

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.