Question

Explain why the answer to |3x - 1| - 5 is all real numbers or (-[infinity], [infinity]).

A. The expression is undefined for all real numbers.
B. The expression has no real solutions.
C. The expression has real solutions for all values of x.
D. The expression has real solutions only for x = 1.

Answer 1

The expression |3x - 1| - 5 has all real numbers as solutions.

Step-by-step explanation:

The expression |3x - 1| - 5 can be written as |3x - 1| + (-5). In this expression, the absolute value of any real number is always positive or zero. Therefore, the expression |3x - 1| - 5 will have all real numbers as solutions. This means that any value of x can be substituted into the expression and it will always result in a real number.