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Solve and check for extraneous solutions please :)

Solve and check for extraneous solutions please :)-example-1
User Vahancho
by
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1 vote

Answer:

There are no extraneous solutions.

7 and -9 are the valid solutions

Explanation:

Given:

  • 3-10|k+1| =-78

To find :

  • Value of k.

Solution:

Isolate the absolute value.


\sf -10|k+1| = -78 - 2


\sf -10|k+1| = -80

Divide both sides by -10.


\sf |k+1| = (-80)/(10)


\sf |k+1| = 8

The absolute value of an expression is its distance from zero.

It has two solutions, one negative and one positive.

The negative solution is:


\sf k+1 = -8

Solving for k, we get:


\sf k = -8-1


\sf k = -9

The positive solution is:


\sf k+1 = 8

Solving for k, we get:


\sf k = 8-1


\sf k = 7

We need to check both solutions to make sure they are not extraneous.

An extraneous solution is a solution that makes the original equation undefined.

Now that we have two potential solutions, k = 7 and k = -9, let's check them in the original equation to see if they are extraneous:

For k = 7:


\sf 2 - 10|7 + 1| = -78


\sf 2 - 10|8| = -78


\sf 2 - 80 = -78


\sf -78 = -78 (True)

For k = -9:


\sf 2 - 10|-9 + 1| = -78


\sf 2 - 10|-8| = -78


\sf 2 - 10*8 = -78


\sf 2 - 80 = -78


\sf -78 = -78 (True)

Both solutions, k = 7 and k = -9, satisfy the original equation, so there are no extraneous solutions.

7 and -9 are the valid solutions to the equation.

User Joe Lissner
by
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