Question

express the following statement in symbols, using <, >, ≤, or ≥. z is at most 7.8. determine the correct symbolic form for the given statement. choose the correct answer. z>7.8 z≥7.8 z≤7.8 z<7.8

Explanation:

Step1: Understand "at most"

"At most" means the value is less than or equal to the given number. So \( z \) can be equal to \( 7.8 \) or less than \( 7.8 \).

Step2: Match with symbols

• \( z > 7.8 \) means \( z \) is greater than \( 7.8 \), which is not "at most".
• \( z \geq 7.8 \) means \( z \) is greater than or equal to \( 7.8 \), which is "at least", not "at most".
• \( z \leq 7.8 \) means \( z \) is less than or equal to \( 7.8 \), which matches "at most".
• \( z < 7.8 \) means \( z \) is strictly less than \( 7.8 \), but "at most" includes equality.

Answer:

\( z \leq 7.8 \) (corresponding to the option with \( z \leq 7.8 \))