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What is the solution to Ix - 2|+ 3 > 17?

What is the solution to Ix - 2|+ 3 > 17?-example-1

2 Answers

0 votes

Answer:x < -12 or x > 16.

Explanation:

User Rohit Falor
by
8.0k points
1 vote

Answer:

x < -12 or x > 16.

Explanation:

We have:

Ix - 2|+ 3 > 17

To solve this equation, we first need to isolate the absolute value term. We do this by subtracting 3 from both sides of the equation, giving us:

Ix - 2|+ 3 -3> 17-3

Ix - 2| > 14

Now, we need to consider two cases: the case where x - 2 is positive, and the case where x - 2 is negative.

  • Case 1: x - 2 is positive.

In this case, we can remove the absolute value bars, because the expression inside the bars is already positive. So, we have:

x - 2 > 14

Adding both side by 2.

x-2+2 > 14+2

x > 16

This means that x > 16.

  • Case 2: x - 2 is negative

In this case, we can write the expression inside the absolute value bars as its negative equivalent. So, we have:

|x - 2| = -(x - 2)

Now, we can remove the absolute value bars, because the expression inside the bars is now negative. So, we have:

-(x - 2) > 14

opening bracket

-x +2 > 14

Adding x on both sides

-x+x+2 > 14+x

2 > 14+ x

Subtracting 14 on both sides

2-14> x

x <-12

This means that x < -12.

Combining the solutions from both cases, we get that x < -12 or x > 16.

Also written as : - 12 > x > 16


\boxed{\textsf{Hope This Helps!!!}}

User Jorge Perez
by
7.5k points

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