Question

Find the value of x+|x| , if x=7,10,0,-3,-8. If x<0

Answer 1

Answer:

14, 20, 0, 0, 0

Step-by-step explanation:

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

|x|=x∣x∣=x if x \geq≥ 0

|x|=-x∣x∣=−x if x < 0

In this problem, we have the expression

x+|x|x+∣x∣

Therefore, we can rewrite it as:

if x ≥ 0:

x+|x|=x+x=2xx+∣x∣=x+x=2x (a)

If x < 0:

x+|x|=x+(-x)=0x+∣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 = 142x=2⋅7=14

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

2x=2\cdot 10=202x=2⋅10=20

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

2x=2\cdot 0=02x=2⋅0=0

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

x+|x|=0x+∣x∣=0

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

x+|x|=0x+∣x∣=0