Mathematics, 16.12.2022 14:00, jayyla32

|x-2|=|4+x|
How can I find the value of X?

Answers: 3

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Answers

answered: tjahaheuuwu

x = -1

Step-by-step explanation:

You want to find the value(s) of x that satisfy the equation |x-2| = |4+x|.

Domains

The behavior of each absolute value function changes at the point where its argument is zero. For this equation, that will be two points:

x -2 = 0 ⇒ x = 2

x +4 = 0 ⇒ x = -4

These two points on the number line divide the domain of the equation into three parts:

x < -4-4 ≤ x < 22 ≤ x.

The behavior of the equation will be different in those three domains.

x < -4

In this domain, both absolute value functions negate their arguments. That means the equation is equivalent to ...

-(x -2) = -(4 +x)

2 = -4 . . . . . . . . . . add x to both sides

This has no solutions: there are no values of x that will make this true.

-4 ≤ x < 2

In this domain, the absolute value function on the left negates its argument, so the equation is equivalent to ...

-(x -2) = (4 +x)

-2 = 2x . . . . . . . . . add x-4 to both sides

-1 = x . . . . . . . . . divide by 2

This value of x is in the domain, so represents a solution to the equation.

x = -1

2 ≤ x

In this domain, neither absolute value function negates its argument, so the equation is equivalent to ...

x -2 = 4 +x

-2 = 4 . . . . . . . subtract x

This has no solutions: there are no values of x that will make this true.

The given equation has one solution: x = -1.

Additional comment

When solving an equation like this graphically, it is often useful to put it in the form f(x) = 0. We can obtain that form by defining ...

f(x) = |x -2| -|4 +x|

The graph of this is attached. The only solution is where f(x) = 0, at x = -1.

Note that the function is parallel to the x-axis outside of the middle domain, so will not have any x-intercepts in those regions.

|x-2|=|4+x|
How can I find the value of X?

answered: Guest

The answer is "a"radius = 12.7 unitsdiameter = radius × 212.7 units × 2 = 25.4 units
The blue segment below is a radius of o. what is the length of the diameter of the circle?

The blue segment below is a radius of o. what is the length of the diameter of the circle?

answered: Guest

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)

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