Answer:
x = 3
Explanation:
To solve the equation F(x) = 2 |x - 3|, we need to consider the absolute value function and find the values of x that satisfy the equation.
The absolute value function, denoted by |x|, gives the distance of x from zero on a number line. For any given number x, |x| is always positive or zero.
In this equation, we have |x - 3|, which means the expression inside the absolute value bars is x - 3. If x - 3 is positive or zero, then |x - 3| = x - 3. If x - 3 is negative, then |x - 3| = -(x - 3), which is equivalent to -x + 3.
Now let's solve the equation by considering these two cases:
1. When x - 3 ≥ 0:
In this case, |x - 3| = x - 3.
So, the equation becomes 2(x - 3) = 0.
Simplifying, we get 2x - 6 = 0.
Solving for x, we find x = 3.
2. When x - 3 < 0:
In this case, |x - 3| = -(x - 3).
So, the equation becomes 2(-(x - 3)) = 0.
Simplifying, we get -2x + 6 = 0.
Solving for x, we find x = 3.
Therefore, the solution to the equation F(x) = 2 |x - 3| is x = 3.