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Write and solve an inequality or multiple inequalities to describe the possible values of [tex][tex]$x$[/tex][/tex].

A. [tex]$x \ \textgreater \ 28$[/tex]
B. [tex]$0 \ \textless \ x \ \textless \ 28$[/tex]
C. [tex][tex]$x \ \textgreater \ 8$[/tex][/tex]
D. [tex]$1 \ \textless \ x \ \textless \ 8$[/tex]


Sagot :

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].
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