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
