how to add |x| +4-x^2
To add the expression |x| + 4 - x^2, we need to consider two cases: one where x is positive or zero, and another where x is negative.
Case 1: x is positive or zero
In this case, the absolute value of x is equal to x. Therefore, we can rewrite the expression |x| + 4 - x^2 as x + 4 - x^2.
Case 2: x is negative
When x is negative, the absolute value of x is equal to -x. Hence, the expression |x| + 4 - x^2 becomes -x + 4 - x^2.
Now, we have two separate expressions depending on the value of x. To find the sum, we need to consider the two cases:
If x is positive or zero (Case 1), the expression is x + 4 - x^2.
If x is negative (Case 2), the expression is -x + 4 - x^2.
So, the final answer is obtained by adding these two cases together:
(x + 4 - x^2) + (-x + 4 - x^2)
Now, simplify the expression by combining like terms:
x + 4 - x^2 - x + 4 - x^2
Combine the x terms:
x - x - x = -x
Combine the constant terms:
4 + 4 = 8
Combine the x^2 terms:
-x^2 - x^2 = -2x^2
Hence, the final sum of the expression |x| + 4 - x^2 is -2x^2 - x + 8.