Final answer:
To find all values of b for the equation √b + 18√= 50, we consider both the positive and negative cases for the absolute value, leading to two answers: b = 32 and b = -68.
Step-by-step explanation:
The student's question involves solving an absolute value equation: √b + 18√= 50. To solve for b, we must consider both the positive and negative scenarios that would satisfy the absolute value.
- For the positive scenario: b + 18 = 50, we solve for b by subtracting 18 from both sides to get b = 32.
- For the negative scenario: -(b + 18) = 50, which simplifies to -b - 18 = 50. Adding 18 to both sides gives -b = 68, and then multiplying by -1 gives b = -68.
Therefore, the solution to the equation √b + 18√= 50 in its simplest form is b = 32 or b = -68.