Sure! Let's analyze each inequality one by one and find the possible values of [tex]\( x \)[/tex] that satisfy each condition.
1. Inequality: [tex]\( x > 28 \)[/tex]
This inequality states that [tex]\( x \)[/tex] must be greater than 28. Since [tex]\( x \)[/tex] cannot be simultaneously greater than 28 and meet the other conditions, this inequality does not provide a feasible solution within the constraints of the other inequalities.
Therefore, the possible values for [tex]\( x \)[/tex] in this case are:
[tex]\[
\text{no solution}
\][/tex]
2. Inequality: [tex]\( 0 < x < 28 \)[/tex]
This inequality states that [tex]\( x \)[/tex] must be greater than 0 and less than 28. The values for [tex]\( x \)[/tex] that satisfy this inequality lie within the interval (0, 28).
Therefore, the possible values for [tex]\( x \)[/tex] in this case are:
[tex]\[
(0, 28)
\][/tex]
3. Inequality: [tex]\( x > 8 \)[/tex]
This inequality states that [tex]\( x \)[/tex] must be greater than 8. The values for [tex]\( x \)[/tex] that satisfy this inequality lie in the interval (8, ∞).
Therefore, the possible values for [tex]\( x \)[/tex] in this case are:
[tex]\[
(8, \infty)
\][/tex]
4. Inequality: [tex]\( 1 < x < 8 \)[/tex]
This inequality states that [tex]\( x \)[/tex] must be greater than 1 and less than 8. The values for [tex]\( x \)[/tex] that satisfy this inequality lie within the interval (1, 8).
Therefore, the possible values for [tex]\( x \)[/tex] in this case are:
[tex]\[
(1, 8)
\][/tex]
In summary, the solutions to the respective inequalities are:
1. [tex]\( x > 28 \)[/tex] leads to no solution.
2. [tex]\( 0 < x < 28 \)[/tex] leads to [tex]\( (0, 28) \)[/tex].
3. [tex]\( x > 8 \)[/tex] leads to [tex]\( (8, \infty) \)[/tex].
4. [tex]\( 1 < x < 8 \)[/tex] leads to [tex]\( (1, 8) \)[/tex].
