How do I solve for the absolute inequality |5-4x|=9?

Question

I know it will be an "or" .. just messed up somewhere in my arithematic

Answer 1

(5-4x) = 9
or
(5-4x) = -9

Solve each:
5 - 4x = 9
-4x = 9 - 5
-4x = 4
x = -1

5 - 4x = -9
-4x = -9 - 5
-4x = -14
x = 14/4
x = 7/2

So x = -1 or x = 3.5

Answer 2

Ok, let's cover all bases.

If you mean |5 - 4x| = 9: there are only two "somethings" that make

|something| = 9

true. Those two somethings are 9 and -9. So whatever is inside the absolute values must equal 9 or -9. Since the thing inside the absolute value is 5 - 4x, you get two equations to solve:

5 - 4x = 9 or 5 - 4x = -9

(not AND: x can't equal two different values at the same time).





If you mean |5 - 4x| < 9: if you understand that "asbolute value" simply means "how far away from zero on the number line", then

|something| < 9

means that "something" cannot be more than 9 units from zero on the number line. This can only happen if

-9 < something AND something < 9,

or more compactly,

-9 < something < 9

Since the something is 5 - 4x, this means you solve

-9 < 5 - 4x AND 5-4x < 9,

or more compactly,

-9 < 5 - 4x < 9






If you mean |5 - 4x| > 9: this means that something has to be MORE than 9 units away from xero on the number line. The only way this can happen is if

something < -9 OR something > 9

(it must be OR: you can't be to the left of -9 ANd to the right of 9 at the same time).

The something here is 5 - 4x, so solve

5 - 4x < -9 OR 5 - 4x > 9.

Answer 3

this is not an inequality. The answer is -1 or 3 1/2

Answer 4

5-4x = 9
-4x = 4
x = 4/ -4
x = -1

Answer 5

│5 - 4x│= 9

5 - 4x = 9

5 - 4x - 5 = 9 - 5

- 4x = 4

-4x/-4 = 4/-4

x = - 1

The answer is x = - 1

- - - - - - - - - - - - - - - - - -

│5 - 4x│ = 9

5- 4x = - 9

5 - 4x - 5 = -9 - 5

- 4x = - 14

-4x/-4 = -14/-4

x = 3.5

- - - - - - - - - - - - - - -

Check

│5 - 4x│= 9

│5 - 4(-1)│ = 9

│5 + 4 │ = 9

│9 │ = 9

9 = 9

- - - - - - - - - - - - - - - -

Check

│5 - 4x│ = 9

│5 - 4(3.5)│ = 9

│5 - 14│= 9

│-9 │ = 9

- (-9) = 9

9=9

- - - - - - - - - - - - - - - -

The solution set is { -1, 3.5 }

- - - - - - - - s

Answer 6

5 - 4x = 9 AND 5 - 4x = -9

Answer 7

5-4x=9 (or) 5-4x=-9
4x=-4 (or) 4x=14
x=-1 (or) x=3.5

i.e:- you will get modulus of some number = 9 if and only if that number is either 9 or -9.

Answer 8

mod(5-4x)=9
therefore it must be either +(5-4x)=9 or -(5-4x)=9
1st case
5-4x=9
x = -1
2nd case
-(5-4x)=9
-5+4x=9
x=7/2
x = -1 or x = 7/2

Answer 9

same as equality

x=-(9-5)/4

Answer 10

Is it an equation or an inequality?