algebra question

Question

28.The absolute value of the difference between 2x and 3 is 6. What are the two possible values of

x?

Answer 1

9/2, - 3/2

Remember, the absolute value of a number IS its value, without respect to the sign. Think of the number line, and the absolute value is a certain number of digits from 0. It can be negative or positive.

Hope this helps!

Answer 2

One way to do this problem is to first write it out:

|2x - 3| = 6

Then, with every absolute value problem comes two problems built into it:

Case 1 is when you replace the absolute value signs with parentheses with a "+" in front of them:

+(2x - 3) = 6 (which is, by the way, just 2x - 3 = 6)

Case 2 is when you replace the absolute value signs with parentheses with a "+" in front of them:

-(2x - 3) = 6 - the negative sign gets distributed to the two elements inside the parentheses to become -2x + 3 = 6

Then you solve both problems:

Case 1:

+(2x - 3) = 6

2x - 3 = 6

2x = 9

x = 4.5

Case 2:

-(2x - 3) = 6

-2x + 3 = 6

-2x = 3

x = -1.5

Answer 3

Gin

The absolute value of the difference is the physical distance between the point x=2x and x=3 on the number line.

As this is 6, it means that the distance between 2x and 3 must be 6. In other words 2x must be 3+6 or 3-6.

Giving x = 4.5 or x = -1.5

Mike