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Answer :
Sure, let's find the solution set to the inequality [tex]\( |x| > 38.1 \)[/tex].
1. Understand what [tex]\( |x| > 38.1 \)[/tex] means:
- The absolute value of [tex]\( x \)[/tex] represents the distance of [tex]\( x \)[/tex] from 0 on the number line.
- If the distance of [tex]\( x \)[/tex] from 0 is greater than 38.1, then [tex]\( x \)[/tex] must be either greater than 38.1 or less than -38.1.
2. Break down the inequality [tex]\( |x| > 38.1 \)[/tex] into two separate inequalities:
- Case 1: [tex]\( x > 38.1 \)[/tex]
- Case 2: [tex]\( x < -38.1 \)[/tex]
3. Combine the two cases:
- We have [tex]\( x > 38.1 \)[/tex] or [tex]\( x < -38.1 \)[/tex].
In conclusion, the solution set of the inequality [tex]\( |x| > 38.1 \)[/tex] is:
[tex]\[ x < -38.1 \text{ or } x > 38.1 \][/tex]
Among the given options:
- A. [tex]\( x \leq 38.1 \)[/tex]
- B. [tex]\( x < -38.1 \text{ or } x > 38.1 \)[/tex]
- C. [tex]\( -38.1 < x < 38.1 \)[/tex]
- D. [tex]\( x < -38.1 \)[/tex]
- E. [tex]\( x > 38.1 \)[/tex]
- F. [tex]\( x < 38.1 \)[/tex]
The correct choice is:
[tex]\[ \text{B. } x < -38.1 \text{ or } x > 38.1 \][/tex]
1. Understand what [tex]\( |x| > 38.1 \)[/tex] means:
- The absolute value of [tex]\( x \)[/tex] represents the distance of [tex]\( x \)[/tex] from 0 on the number line.
- If the distance of [tex]\( x \)[/tex] from 0 is greater than 38.1, then [tex]\( x \)[/tex] must be either greater than 38.1 or less than -38.1.
2. Break down the inequality [tex]\( |x| > 38.1 \)[/tex] into two separate inequalities:
- Case 1: [tex]\( x > 38.1 \)[/tex]
- Case 2: [tex]\( x < -38.1 \)[/tex]
3. Combine the two cases:
- We have [tex]\( x > 38.1 \)[/tex] or [tex]\( x < -38.1 \)[/tex].
In conclusion, the solution set of the inequality [tex]\( |x| > 38.1 \)[/tex] is:
[tex]\[ x < -38.1 \text{ or } x > 38.1 \][/tex]
Among the given options:
- A. [tex]\( x \leq 38.1 \)[/tex]
- B. [tex]\( x < -38.1 \text{ or } x > 38.1 \)[/tex]
- C. [tex]\( -38.1 < x < 38.1 \)[/tex]
- D. [tex]\( x < -38.1 \)[/tex]
- E. [tex]\( x > 38.1 \)[/tex]
- F. [tex]\( x < 38.1 \)[/tex]
The correct choice is:
[tex]\[ \text{B. } x < -38.1 \text{ or } x > 38.1 \][/tex]
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