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Solve for x: |2x + 6| − 4 = 20

Sagot :

The answers are in the attachment below. x=9, and x=-15.
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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!! :)

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