Question

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

Explanation:

Step1: Understand the problem

Laurie's current depth is -30 feet. She wants to stay within 10 feet of this depth. Let \( x \) be the depth she is at (the depth we want to find the range for). The difference between her current depth (-30) and the depth \( x \) should be within -10 and 10 (since within 10 feet means the absolute difference is at most 10). So, \( |x - (-30)| = 10 \), which can be rewritten as \( |x + 30| = 10 \). By the definition of absolute value, this gives two equations: \( x + 30 = 10 \) (which is equivalent to \( - 30+x=10 \)) and \( x + 30=- 10 \) (which is equivalent to \( -30 + x=-10 \)).

Step2: Analyze each option

• Option 1: The equations \( -30 - x = 10 \) and \( -30 - x=-10 \) do not represent the correct relationship. The difference should be between \( x \) and -30, not -30 and \( x \) in this form.
• Option 2: The equations \( -30 + x = 10 \) and \( -30 + x=-10 \) are equivalent to \( x+30 = 10 \) and \( x + 30=-10 \), which come from the absolute - value equation \( |x + 30| = 10 \), representing the depth \( x \) being within 10 feet of -30.
• Option 3: The equations \( x + 10 = 30 \) and \( x + 10=-30 \) do not relate to the problem of Laurie's depth being within 10 feet of -30.
• Option 4: The equations \( x - 10 = 30 \) and \( x - 10=-30 \) also do not represent the correct relationship for Laurie's diving depth.

Answer:

-30 + x = 10 and -30 + x = -10 (the second option)