Mathematics, 26.07.2019 10:50 boo6931

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

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Answer from: KetaFord1978

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.

Answer from: Quest

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

=3x+1

=3(2)+1

since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

=x+1

=2+1

now, let's find g(2)g(2):

g(x)

g(2)

=2x

=2⋅2

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

Answer from: Quest

step-by-step explanation:

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