Final answer:
To solve the absolute value equation |x|+5=11, we consider the two cases for x, resulting in x = 6 and x = -6 as the solutions.
Step-by-step explanation:
The problem |x|+5=11 is an equation involving the absolute value of a variable x. To find all solutions, we must consider the nature of absolute value, which is the distance a number is from zero on the number line, regardless of direction. This means the inside of the absolute value, x, could be either positive or negative and still produce the same outcome after applying absolute value.
To solve the equation, we set up two separate equations by considering both the positive and negative scenarios of x:
- x + 5 = 11, which simplifies to x = 6 after subtracting 5 from both sides.
- -(x) + 5 = 11, which simplifies to -x = 6 after subtracting 5 from both sides, and then further simplifies to x = -6 after multiplying each side by -1.
As a result, the solutions to the given equation are x = 6 and x = -6.