Question

laurie is trying to stay within 10 feet of her current diving depth of (-30) feet (with regard to sea level) is still good but she can be close to the sea life during her scuba dive. which two equations can be u minimum and maximum depths laurie wants to stay between?
(\bigcirc) (-30 - x = 10) and (-30 - x = -10)
(\bigcirc) (-30 + x = 10) and (-30 + x = -10)
(\bigcirc) (x + 10 = 30) and (x + 10 = -30)
(\bigcirc) (x - 10 = 30) and (x - 10 = -30)

Explanation:

Step1: Define the variable

Let \( x \) be Laurie's diving depth. She wants to stay within 10 feet of -30 feet. So the difference between her depth \( x \) and -30 should be at most 10 in absolute value, i.e., \( |x - (-30)|=|x + 30| = 10\) (wait, no, actually the distance from \( x \) to -30 is within 10, so \( |x-(-30)|\leq10\), but we need the equations for minimum and maximum, so when \( |x + 30|=10\), we can split into two cases: \( x+30 = 10\) and \( x + 30=- 10\), which can be rewritten as \(x=-30 + 10\) and \(x=-30-10\), or in the form of \( - 30+x=10\) (when solving for maximum, \(x=-30 + 10\) is maximum? Wait, no, depth is negative, so -30 + 10=-20 (less deep, closer to surface) and -30 - 10=-40 (deeper). So the equations for the boundaries (minimum and maximum) are when \(x-(-30)=10\) (i.e., \(x + 30 = 10\) or \( - 30+x=10\)) and \(x-(-30)=- 10\) (i.e., \(x + 30=-10\) or \( - 30+x=-10\)). So the two equations are \( - 30+x = 10\) and \( - 30+x=-10\).

Step2: Analyze each option

• Option 1: \(-30 - x=10\) and \(-30 - x=-10\) → Solving gives \(x=-40\) and \(x=-20\) but the form is wrong, should be \(x - (-30)\) not \(-30 - x\).
• Option 2: \(-30 + x=10\) and \(-30 + x=-10\) → This is correct as it represents \(x=-30 + 10\) (maximum depth, -20) and \(x=-30-10\) (minimum depth, -40).
• Option 3: \(x + 10=30\) and \(x + 10=-30\) → Solving gives \(x = 20\) and \(x=-40\), 20 is positive (above sea level) which is not possible for diving depth.
• Option 4: \(x - 10=30\) and \(x - 10=-30\) → Solving gives \(x = 40\) and \(x=-20\), 40 is positive, not possible.

Answer:

B. \(-30 + x = 10\) and \(-30 + x=-10\) (assuming the second option in the list is this one, as per the options given: the second option is \(-30 + x = 10\) and \(-30 + x=-10\))