Let's solve the given equation step-by-step:
The equation we have is:
[tex]\[ |4x - 6| = -10 \][/tex]
1. Understanding Absolute Value:
- The absolute value of a number is always non-negative. It represents the distance of a number from zero on the number line, which cannot be negative.
- Therefore, the expression [tex]\( |4x - 6| \)[/tex] represents the distance from zero and must always be non-negative.
2. Analyzing the Given Equation:
- The right-hand side of the equation is [tex]\(-10\)[/tex], which is a negative number.
- Since the absolute value (which is always non-negative) is set equal to a negative number, this situation is impossible.
3. Conclusion:
- An absolute value expression can never equal a negative number, since it represents a distance (which is always non-negative).
- Therefore, there are no values of [tex]\( x \)[/tex] that can satisfy the equation [tex]\( |4x - 6| = -10 \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{\text{There are no solutions.}} \][/tex]
