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How do I solve this?

How do I solve this?-example-1

1 Answer

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Answer:

x is in the range [-1,4]

Explanation:

I haven't worked with absolute value inequalities in awhile, but let's take a wack at this.

We are given the following inequality:

| 2x - 3 | <= 5

This implies two possible cases:

[1] -5 <= 2x -3

Or

[2] 2x - 3 <= 5

So let's solve x for both of these cases:

[1] -5 <= 2x - 3

-2 <= 2x

-1 <= x

[2] 2x - 3 <= 5

2x <= 8

x <= 4

So from these cases, we can say the following is true:

x >= -1 and x <= 4

Thus, we can write this in the form

-1 <= x <= 4

Or in interval notation:

x is element of reals

Also written as

x is in the range [-1,4]

Where the closed brackets represent 1 and 4 as possible answers whereas parenthesis would imply they were not.

Cheers.

User Romaric
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