Solve for x: lx-1I = 3.?

Question

Ix-1I is an absoloute value, I could not find a symbol on the keyboard so I used a capital "I" inplace.

Also:

Solve the inequality:

I2x+3I <= 2

"It reads abosolute value 2x plus 3 is less than or equal to 2"

Answer 1

Absolute value means that whatever number is within the bars, you make it positive. Therefore you want x-1 to equal 3 or -3 because once you take the absolute value, you will have 3 either way.
If x-1 = 3 or x-1 = -3, then x= -2 or 4

Solve the next equation the same way:
so that 2x+3 gives you 2 and -2.
2x+3 <= 2 and 2x+3 <= -2

Solving these you find that x<= -1/2 or x<= -5/2, which gives you the range -5/2<=x <= -1/2

Answer 2

First solving the first one.

Ix-1I = 3
gives x-1 = 3, -3
First taking 3 and solving.
x-1 = 3 implies x = 4

Now taking -3,
x-1 = -3 implies x = -2.

Therefore the solution for the first question is x = -2 and 4.

Now commimg to the second one.
The given inequality can be written as
-2 <= 2x+3 <= 2 , According to the definition of modulus.
subtracting 3 in the above equation, gives
-5 <= 2x <= -1
Now dividing with 2, gives
-5/2 <= x <= -1/2.

Therefore x belongs to the interval, (-5/2,-1/2)
This can also be written as (-2.5,-0.5)

Hope you can understand the above explaination.

Answer 3

Okay. When you find the absolute value of a number, it is always positive. For example:

| 1 | = 1, | -1 | = 1

This being said, you need to split this into two equations. You have to take into account, what if the equation inside the absolute value is negative.

| x - 1 | = 3

x - 1 = 3
x = 4

-(x - 1) = 3
-x + 1 = 3
-x = 2
x = -2

The answers are 4, -2.

Next. Same thing.

| 2x + 3 | <= 2

2x + 3 <= 2
2x <= -1
x <= -1/2

-(2x + 3) <= 2
-2x - 3 <= 2
-2x <= 5
x <= -5/2

Your answer is:
x <= -1/2, x <= -5/2

If you need any more help, feel free to click the avatar next to my name, then click contact me. You can email me your questions. I would be glad to help.

Answer 4

A)
|x - 1| = 3

x - 1 = +3 or x - 1 = -3
x = 4 or x = -2


B)
|2x + 3| <= 2
2x + 3 <= +2 or 2x + 3 >= -2
x <= (-1/2) or x >= (-5/2)

which means x is between -1/2 and -5/2, (-5/2 <= x <= -1/2)

Answer 5

|x - 1| = 3 , x - 1 = 3 or x - 1 = -3 , x = 4 or x = -2


|2x + 3| <= 2 , -2 <= 2x + 3 <= 2 , -5 <= 2x <= -1 ,

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

Answer 6

Just set x-1 = 3, then x-1 = -3. You get 4 and -2.

For the inequality, split it into

-2 <= 2x+3 <= 2.

Sub. 3 from each end: -5<= 2x <= -1.

Div. thru by 2: -2.5 <= x <= -.5

Answer 7

The symbol on the keyboard is Shift-\. You should find the \ above the Enter/return key or below it, depending on the version and age of your keyboard. If your keyboard is for Mac, I don't think there is a \ key there...

x = 4 for problem 1.
x≤-0.5 and x≥-2.5 for problem 2.

Answer 8

|x-1|=3
x-1=3 or x-1=-3
x=3+1 or x=-3+1
x=4 or x=-2

|2x+3|<=2
-2<=2x+3<=2
-2-3<=2x<=2-3
-5<=2x<=-1
-5/2<=x<=-1/2
-2.5<=x<=-0.5 or in fractions, -2 and1/2 <=x<=-1/2

Answer 9

Ix-1I=3 then

Ix=3+1I then

x=(3+I)/l

Answer 10

| x |=4

|2x+3| < 2
-3
| 2x | <-1
/2
| x | < -1\2