Find the value of the expression x+|x|, if x=7, 10, 0, −3, −8. Simplify the expression x+|x|, if:
x≥0
if x ≥ 0, then x + |x|=
we just did one of these. What is your difficulty here?
Just use the definition of |x| that I gave you.
If x ≥ 0, then the value of |x| is equal to x. Therefore, the expression x + |x| simplifies to:
x + |x| = x + x = 2x
If x ≥ 0, then the absolute value of x is equal to x itself. So, the expression x + |x| simplifies to 2x.
Let's plug in the given values of x and simplify:
For x = 7:
2x = 2 * 7 = 14
For x = 10:
2x = 2 * 10 = 20
For x = 0:
2x = 2 * 0 = 0
For x = -3:
Since x < 0, the absolute value of x is -x. So, x + |x| becomes -3 + |-3| = -3 + 3 = 0.
For x = -8:
Since x < 0, the absolute value of x is -x. So, x + |x| becomes -8 + |-8| = -8 + 8 = 0.
Therefore, the simplified expression x + |x| for x ≥ 0 is always equal to 2x.