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?

A. x + 30 = 10 and x + 30 = –10
B. x – 30 = 10 and x – 30 = –10
C. x + 10 = 30 and x + 10 = –30
D. x – 10 = 30 and x – 10 = –30

Answer 1

ANSWER
A. x + 30 = 10 and x + 30 = –10

Step-by-step explanation
If x represents the depth of Laurie at a given moment, then the distance between his current depth and -30 feet is given by

| x - (-30) |

which can be simplifed into

| x + 30 |

We use absolute value because distance cannot be negative.

Laurie must stay within 10 feet. Therefore, the distance x is from -30 feet has to be equal to 10 to find the maximum and minimum depths that Laurie can stay between:

| x + 30 | = 10

When we solve this absolute value equation, we work with two cases.

Case 1: When x + 30 is positive, then |x+30| = x+30 (no change) and we have the equation
x + 30 = 10

Case 2: When x + 30 is negative, then |x+30| = -(x+30) so as to force the distance into a positive number. Then this gives us the equation
-(x+30) = 10
which we can multiply both sides by -1 to get
x + 30 = -10