Question

1. two divers are underwater. one diver is at a depth of 32 meters. the other diver’s depth, x, satisfies the equation: | 2x - 32 | = 10 the other diver’s smallest depth is ______ meters.

Explanation:

Step1: Solve the absolute - value equation

For an absolute - value equation \(|A| = B\) (where \(B\geq0\)), the solutions are given by \(A = B\) or \(A=-B\).
Given the equation \(|2x - 32|=10\), we can split it into two equations:

1. \(2x-32 = 10\)
2. \(2x - 32=- 10\)

Step2: Solve the first equation \(2x-32 = 10\)

Add 32 to both sides of the equation:
\(2x-32 + 32=10 + 32\)
\(2x=42\)
Divide both sides by 2:
\(x=\frac{42}{2}=21\)

Step3: Solve the second equation \(2x - 32=-10\)

Add 32 to both sides of the equation:
\(2x-32 + 32=-10 + 32\)
\(2x = 22\)
Divide both sides by 2:
\(x=\frac{22}{2}=11\)

Step4: Find the smallest depth

We have two solutions for \(x\): \(x = 21\) and \(x = 11\).
To find the smallest depth, we compare the two values. Since \(11<21\), the smallest depth is 11 meters.

Answer:

11