Why is the equation - 2|x+4|=6 have no solution

Remember this first.

The solution of an equation is the value or values that make the equation a true statement.

With this equation, we are looking for any value we can replace x with that will make the following equation true.

-2|x + 4| = 6

Start by dividing both sides by - 2.

You get

|x + 4| = - 3

The equation above states that if you take the absolute value of the sum of a a number and 4, you get - 3. That is impossible because the absolute value of a number can never be negative.

If you take the absolute value of zero, you get zero. If you take the absolute value of a positive number, it's just the positive number. If you take the absolute value of a negative number, you get the opposite of that negative number, which is a positive number. An absolute value can only be positive or zero. It can never be negative.

No matter what number you choose for x, once you add that number to 4 and take the absolute value of the sum, you will never get a negative answer. Therefore, there is no value of x that will make this equation true. That is why there is no solution.