Question

rewriting a compound inequality
the compound inequality ( 8.00 leq x < 9.50 ) represents all values, ( x ), for which college students are paid hourly as teacher assistants. what is another way of writing this compound inequality?
( circ ) ( x leq 8.00 ) and ( x < 9.50 )
( circ ) ( x leq 8.00 ) or ( x < 9.50 )
( circ ) ( x geq 8.00 ) and ( x < 9.50 )
( circ ) ( x geq 8.00 ) or ( x < 9.50 )

Explanation:

Step1: Analyze the original inequality

The compound inequality is \(8.00 \leq x < 9.50\). This means \(x\) is greater than or equal to \(8.00\) and \(x\) is less than \(9.50\). In inequality terms, \(x \geq 8.00\) (since \(8.00\leq x\) is equivalent to \(x\geq8.00\)) and \(x < 9.50\).

Step2: Match with the options

• Option 1: \(x\leq8.00\) and \(x < 9.50\) is incorrect because the original inequality requires \(x\) to be at least \(8.00\), not at most.
• Option 2: \(x\leq8.00\) or \(x < 9.50\) is incorrect. The "or" here is wrong because \(x\) must satisfy both conditions, not just one of them, and also the first part about \(x\leq8.00\) is wrong.
• Option 3: \(x\geq8.00\) and \(x < 9.50\) matches our analysis. The "and" is correct because \(x\) has to satisfy both being greater than or equal to \(8.00\) and less than \(9.50\).
• Option 4: \(x\geq8.00\) or \(x < 9.50\) is incorrect. The "or" is wrong because \(x\) needs to satisfy both conditions simultaneously, not just one of them.

Answer:

C. \(x\geq 8.00\) and \(x < 9.50\) (assuming the options are labeled A, B, C, D with C being \(x\geq 8.00\) and \(x < 9.50\))