Question

graph this compound inequality: ( x < 8.3 ) or ( x > 9.8 )
the compound inequality could represent which scenario?

• if janie scores between 8.3 and 9.8 in her gymnastics performance, she qualifies for the next level.
• ms. choy spent a minimum of $8.30 per person at a dinner party.
• tranh must remake any sculptures that weigh less than 8.3 pounds or more than 9.8 pounds.
• nathaniel earns at most $9.80 per hour worked.

Explanation:

Part 1: Graphing the compound inequality \( x < 8.3 \) or \( x > 9.8 \)

The compound inequality \( x < 8.3 \) or \( x > 9.8 \) consists of two separate inequalities.

• For \( x < 8.3 \), we draw an open circle at \( 8.3 \) (since \( x \) is not equal to \( 8.3 \)) and shade to the left of \( 8.3 \).
• For \( x > 9.8 \), we draw an open circle at \( 9.8 \) (since \( x \) is not equal to \( 9.8 \)) and shade to the right of \( 9.8 \).

The given number line already has open circles at \( 8.3 \) (around the 8.3 mark) and \( 9.8 \) (around the 9.8 mark) with shading to the left of \( 8.3 \) and to the right of \( 9.8 \), which matches the graph of \( x < 8.3 \) or \( x > 9.8 \).

Part 2: Determining the scenario represented by the compound inequality

• First option: "If Janie scores between 8.3 and 9.8...", this would be represented by \( 8.3 < x < 9.8 \), not \( x < 8.3 \) or \( x > 9.8 \). Eliminate.
• Second option: "Ms. Choy spent a minimum of $8.30 per person...", this would be \( x \geq 8.30 \), not the given compound inequality. Eliminate.
• Third option: "Tranh must remake any sculptures that weigh less than 8.3 pounds or more than 9.8 pounds", this is exactly \( x < 8.3 \) or \( x > 9.8 \), which matches the compound inequality.
• Fourth option: "Nathaniel earns at most $9.80 per hour...", this would be \( x \leq 9.80 \), not the given compound inequality. Eliminate.

Answer:

s:

• The graph of \( x < 8.3 \) or \( x > 9.8 \) is correctly represented by the given number line (open circles at 8.3 and 9.8, shading left of 8.3 and right of 9.8).
• The scenario represented by the compound inequality is: Tranh must remake any sculptures that weigh less than 8.3 pounds or more than 9.8 pounds.