if x is an integer what is the solution for |2-x|=9?

Question

Do not under stand how to work out. please help

Answer 1

An easier way to remember how to do this is to set the equation to equal a positive number and then a negative number. Like this:

 

2-x=9      And    2-x=-9

 

then solve for x. Your answers are (-7,11) 

 

so, whenever an equation has an absolute value such as this one, just set the equation up first to equal a negative then to equal a positive .

 

 

 

 

Answer 2

The term on the left side is an absolute value so abs(2-x) can take on two possible values.

 

(2-x) if (2-x) > 0, (x-2) if (2-x) < 0. 

 

We have two equations:

 

(1) 2-x=9

 

(2) x-2=9

 

(1)x = -7

 

(2)x = 11.

 

The solution set is x = {-7,11}.

 

To verify this, plug the solutions back into the original equation.

 

abs(2-(-7))=abs(9)=9.

 

abs(2-11)=abs(-9)=9.

 

 

Answer 3

|2-x| = 9

 

+(2-x) = 9 or –(2-x) = 9 because absolute value changes negative to positive.

 

2-x = 9 or 2-x = –9

 

–x = 7 or –x = –11

 

x = –7 or x = 11

Answer 4

The absolute value is really a shorthand way of specifying a piecewise continuous function and is:

 

for x>2, is equal to x-2=9 so x=11, for x<2, is equal to 2-x=9 so x=-7 so the integer solutions are x=11 and -7.

 

Another way to look at this is using an alternate form of the absolute value function i.e. |2-x|=√(2-x)² now set this equal to 9 and solve you easily get x=11 and -7.

 

Hope this helps

 

Jim