Question

Find the value of the expression x+|x|, if x=7, 10, 0, −3, −8. Simplify the expression x+|x|, if:

Answer 1

Answer:

14, 20, 0, 0, 0

Step-by-step explanation:

The notation $|x|$ indicates the absolute value of x, therefore it can be rewritten as:

$|x|=x$ if x $\geq$ 0

$|x|=-x$ if x < 0

In this problem, we have the expression

$x+|x|$

Therefore, we can rewrite it as:

if x ≥ 0:

$x+|x|=x+x=2x$ (a)

If x < 0:

$x+|x|=x+(-x)=0$ (b)

So now we can substitute the given values into the two expressions:

x = 7 (positive value, so we use expression (a):

$2x=2\cdot 7 = 14$

x = 10 (positive values, so we use expression (a):

$2x=2\cdot 10=20$

x = 0 (zero, so we can use expression (a):

$2x=2\cdot 0=0$

x = -3 (negative value, so we use expression (b):

$x+|x|=0$

x = -8 (negative value, so we use expression (b):

$x+|x|=0$