Answer :
To solve the inequality [tex]\( |x| > 38.1 \)[/tex], we need to understand what the absolute value function represents and how it affects the inequality.
The absolute value [tex]\( |x| \)[/tex] represents the distance of [tex]\( x \)[/tex] from 0 on the number line. So, [tex]\( |x| > 38.1 \)[/tex] means the distance of [tex]\( x \)[/tex] from 0 is greater than 38.1.
For [tex]\( |x| \)[/tex] to be greater than 38.1, [tex]\( x \)[/tex] must be either:
1. Greater than 38.1 (i.e., [tex]\( x > 38.1 \)[/tex]), or
2. Less than -38.1 (i.e., [tex]\( x < -38.1 \)[/tex])
These two conditions cover all the values of [tex]\( x \)[/tex] that are more than 38.1 units away from 0. Therefore, the values of [tex]\( x \)[/tex] that satisfy the inequality [tex]\( |x| > 38.1 \)[/tex] are those that either lie to the right of 38.1 on the number line or to the left of -38.1.
Thus, the solution set of the inequality [tex]\( |x| > 38.1 \)[/tex] is [tex]\( x < -38.1 \)[/tex] or [tex]\( x > 38.1 \)[/tex].
Summarizing this step-by-step:
1. Understand the definition of absolute value: [tex]\( |x| \)[/tex] represents the distance of [tex]\( x \)[/tex] from 0.
2. Interpret the inequality [tex]\( |x| > 38.1 \)[/tex]: [tex]\( x \)[/tex] must be more than 38.1 units away from 0.
3. Break down the inequality: This means either [tex]\( x > 38.1 \)[/tex] or [tex]\( x < -38.1 \)[/tex].
4. Combine the solutions: The complete solution set is [tex]\( x < -38.1 \)[/tex] or [tex]\( x > 38.1 \)[/tex].
Therefore, the correct choice for the solution set of the inequality [tex]\( |x| > 38.1 \)[/tex] is:
B. [tex]\( x < -38.1 \)[/tex] or [tex]\( x > 38.1 \)[/tex]
The absolute value [tex]\( |x| \)[/tex] represents the distance of [tex]\( x \)[/tex] from 0 on the number line. So, [tex]\( |x| > 38.1 \)[/tex] means the distance of [tex]\( x \)[/tex] from 0 is greater than 38.1.
For [tex]\( |x| \)[/tex] to be greater than 38.1, [tex]\( x \)[/tex] must be either:
1. Greater than 38.1 (i.e., [tex]\( x > 38.1 \)[/tex]), or
2. Less than -38.1 (i.e., [tex]\( x < -38.1 \)[/tex])
These two conditions cover all the values of [tex]\( x \)[/tex] that are more than 38.1 units away from 0. Therefore, the values of [tex]\( x \)[/tex] that satisfy the inequality [tex]\( |x| > 38.1 \)[/tex] are those that either lie to the right of 38.1 on the number line or to the left of -38.1.
Thus, the solution set of the inequality [tex]\( |x| > 38.1 \)[/tex] is [tex]\( x < -38.1 \)[/tex] or [tex]\( x > 38.1 \)[/tex].
Summarizing this step-by-step:
1. Understand the definition of absolute value: [tex]\( |x| \)[/tex] represents the distance of [tex]\( x \)[/tex] from 0.
2. Interpret the inequality [tex]\( |x| > 38.1 \)[/tex]: [tex]\( x \)[/tex] must be more than 38.1 units away from 0.
3. Break down the inequality: This means either [tex]\( x > 38.1 \)[/tex] or [tex]\( x < -38.1 \)[/tex].
4. Combine the solutions: The complete solution set is [tex]\( x < -38.1 \)[/tex] or [tex]\( x > 38.1 \)[/tex].
Therefore, the correct choice for the solution set of the inequality [tex]\( |x| > 38.1 \)[/tex] is:
B. [tex]\( x < -38.1 \)[/tex] or [tex]\( x > 38.1 \)[/tex]
