Okay so I did the math.
1. Two solutions were found :<span><span>
z=-1
</span><span>z=2/3
</span></span><span>Step 1 :</span>Rearrange this Absolute Value Equation
Absolute value equalitiy entered
|2z-3| = 4z-1
<span>Step 2 :</span>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<span> |2z-3|
</span>For the Negative case we'll use -(2z-3)
For the Positive case we'll use (2z-3)
<span>Step 3 :</span>Solve the Negative Case
-(2z-3) = 4z-1
Multiply
-2z+3 = 4z-1
Rearrange and Add up
-6z = -4
Divide both sides by 6
-z = -(2/3)
Multiply both sides by (-1)
z = (2/3)
Which is the solution for the Negative Case
<span>Step 4 :</span>Solve the Positive Case
(2z-3) = 4z-1
Rearrange and Add up
-2z = 2
Divide both sides by 2
-z = 1
Multiply both sides by (-1)
z = -1
Which is the solution for the Positive Case
Step 5 :Wrap up the solution
<span> z=2/3
</span><span> z=-1
2. </span>-6 < x < 26/3
<span>Step 1 :</span>Rearrange this Absolute Value Inequality
Absolute value inequalitiy entered
|3x-4|+5 < 27
Another term is moved / added to the right hand side.
|3x-4| < 22
<span>Step 2 :</span>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<span> |3x-4|
</span>For the Negative case we'll use -(3x-4)
For the Positive case we'll use (3x-4)
<span>Step 3 :</span>Solve the Negative Case
-(3x-4) < 22
Multiply
-3x+4 < 22
Rearrange and Add up
-3x < 18
Divide both sides by 3
-x < 6
Multiply both sides by (-1)
Remember to flip the inequality sign
x > -6
Which is the solution for the Negative Case
<span>Step 4 :</span>Solve the Positive Case
(3x-4) < 22
Rearrange and Add up
3x < 26
Divide both sides by 3
x < (26/3)
Which is the solution for the Positive Case
<span>Step 5 :</span>Wrap up the solution
-6 < x < 26/3
Solution in Interval Notation
(-6,26/3)
HOPE THIS HELPS :D
