Final answer:
The equation 3|2-x|=-6 has no solution because the absolute value operation output cannot be negative, and therefore cannot be multiplied by 3 to give -6.
Step-by-step explanation:
First, let's look at the equation given: 3|2-x|=-6. The absolute value of a number is always non-negative, meaning the expression inside the absolute value, when multiplied by any non-zero number, cannot equal a negative value. Therefore, this equation has no solution because 3|2-x| cannot yield a negative result like -6.
To theoretically proceed with solving an equation of this structure, you would start by isolating the absolute value part:
- Divide both sides of the equation by the number outside of the absolute value, providing the result is non-negative.
- Drop the absolute value brackets and solve the resulting expression for the variable, but in this case, the process stops as the initial division is not possible.
In summary, no real value of x satisfies the equation 3|2-x|=-6 due to the properties of absolute value yielding non-negative results only.