|2*z - 9| = 1 how do i find z in this equation?

Let's solve your equation step-by-step.

|2z − 9| = 1

Solve Absolute Value.

|2z − 9| = 1

We know either 2z − 9 = 1 or 2z − 9 = −1

2z − 9 = 1 (1 is a possibility)

2z − 9 + 9 = 1 + 9 (Add 9 to both sides)

2z = 10

2z /2  =  10 /2   (Divide both sides by 2)

z=5

2z − 9 = −1 (Possibility 2)

2z − 9 + 9 = −1 + 9  (Add 9 to both sides)

2z = 8

2z /2   =   8 /2   (Divide both sides by 2)

z = 4

1

Two solutions were found :

    z=5

    z=4

Absolute Value Equation entered :

     |2z-9|=1

Step by step solution :

Step  1  :

Rearrange this Absolute Value Equation

Absolute value equalitiy entered

     |2z-9| = 1

Step  2  :

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2z-9|

For the Negative case we'll use -(2z-9)

For the Positive case we'll use (2z-9)

Step  3  :

Solve the Negative Case

     -(2z-9) = 1

    Multiply

     -2z+9 = 1

    Rearrange and Add up

     -2z = -8

    Divide both sides by 2

     -z = -4

    Multiply both sides by (-1)

     z = 4

    Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

     (2z-9) = 1

    Rearrange and Add up

     2z = 10

    Divide both sides by 2

     z = 5

    Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

z=4

z=5

brainliest plzz

step-by-step explanation: