Question

write an equation for the statement: the absolute value of the product of 6 and x equals 48.
6|x| = 48
6x = |48|
|6x| = 48
6x = 48

Explanation:

Step1: Analyze the statement

The statement is "The absolute value of the product of 6 and x equals 48". The product of 6 and x is \(6x\), and we take its absolute value, then set it equal to 48.

Step2: Match with options

• Option 1: \(6|x| = 48\) represents 6 times the absolute value of x, not the absolute value of the product of 6 and x.
• Option 2: \(6x=|48|\) is 6x equals the absolute value of 48 (which is 48), not the absolute value of 6x.
• Option 3: \(|6x| = 48\) means the absolute value of the product of 6 and x is 48, which matches the statement.
• Option 4: \(6x = 48\) is a linear equation without an absolute value, so it doesn't match.

Answer:

The correct option is the third one (the option with \(|6x| = 48\))