If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions.
we have
\(x \ \textless \ 5 \\ x \ \textgreater \ c\)
we know that
The solution is the intersection of both solution sets of the given inequalities.
The solutions of the compound inequality must be solutions of both inequalities.
The value of c could be 5 or any number greater than 5, such that there are no solutions to the compound inequality
Because
A number cannot be both less than 5 and greater than 5 at the same time
therefore
the answer is
for \(c \geq 5\) there are no solutions to the compound inequality
Inequalities are used to relate unequal expressions.
A possible value of x, where the inequality has no solution is 7.
The compound inequality is given as:
\(\mathbf{x < 5\ and\ x > c}\)
Rewrite as:
\(\mathbf{5 > x\ and\ x > c}\)
Merge the inequalities
\(\mathbf{5 > x > c}\)
For the above inequality to be true, the value of c must be less than 5 and x.
So, a possible value of x, where the inequality has no solution is 7.
Because 7 is greater than 5
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