Solve For x: |x-1|<=5/2?

Question

Please help ready to fail Algebra II class.....

Answer 1

|x-1| <= 5/2
means x-1 <= 5/2 and x-1 >=-5/2

means x <= 7/2 and > - 3/2

or -3/2 <= x <= 7/2

Answer 2

|x - 1| <= 5/2
First divide into the three separate equations hidden by the absolute value sign. If (x - 1)> 0, x - 1 is positive and <= 5/2. If x - 1 < 0, -(x -1), 1 - x is positive and less than 5/2. If x - 1 = 0, x = 1, and satisfies the equation.

Now, if 0 < x -1<=5/2, adding one to all three sides of the inequality shows that x must be greater than one and less than or equal to 5/2 +1, or 7/2. So this inequality becomes 1 < x <= 7/2. Since x can also equal 1, we combine the zero case into this inequality and get 1 <= x <=5/2.

This leaves the negative case. 0 < 1 - x <= 5/2. Multiply the inequalities by -1, and flip to get the positive inequality. So, -5/2 <= x -1 < 0. Now adding 1 to all three statements, -3/2 <= x < 1. x = 1 is exactly the lower boundary for the previous case, so we can put both inequalities together to get -3/2<= x <= 7/2.

Answer 3

-5/2= -3/2 = < x <=7/2

Answer 4

For |x-1| <= 5/2, separate into two equations:

x-1 <= 5/2 and x-1 >= -5/2

x <= 5/2 + 1 and x >= (-5/2) + 1

x <= 7/2 and x >= (-3/2)

Answer 5

Been a whilst considering the fact that I surely have performed those. First minus a million from the two edge. you should get 5<_ (5/2)x<15. next you should divide the two edge through five/2. 2_

Answer 6

|x-1| <= 5/2

x-1 <= 5/2 and x-1>= -5/2

x <= 7/2 and x >= -3/2

Result: -3/2 <= x <= 7/2

Answer 7

5/2 = 2.5

You need to do this twice: once for the case with x-1 is negative and once for the case with x-1 is positive:

x-1 is :Positive

x-1<=5/2
(Add one to both sides)
x<=2.5 +1
x<=3.5

x-1 is negative:
x-1>=-2.5
(Add one to both sides)
x>=-1.5

So: X >=-1.5 and x<=3.5

Answer 8

x-1≤5/2
x≤5/2+2/2
x≤7/2

x-1≤-5/2
x≤-5/2+2/2
x≤-3/2

-3/2≤x≤7/2