Mathematics, 03.12.2019 22:31 saabrrinnaaa

1.solve the equation. check for extraneous solutions.
|2z - 3| = 4z -1

2. solve each inequality. graph the solutions.
|3x -4| + 5 < (or equal to) 27

Answers: 1

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Answer from: sierravick123owr441

Okay so I did the math.

1. Two solutions were found :
z=-1
z=2/3
Step 1 :Rearrange this Absolute Value Equation

Absolute value equalitiy entered
|2z-3| = 4z-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-3|

For the Negative case we'll use -(2z-3)

For the Positive case we'll use (2z-3)

Step 3 :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

Step 4 :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

z=2/3
z=-1

2. -6 < x < 26/3

Step 1 :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

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 |3x-4|

For the Negative case we'll use -(3x-4)

For the Positive case we'll use (3x-4)

Step 3 :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

Step 4 :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

Step 5 :Wrap up the solution

-6 < x < 26/3

Solution in Interval Notation

(-6,26/3)

HOPE THIS HELPS :D

Answer from: Quest

$75.00

step-by-step explanation:

i = prt

i = 1,5000 * 0.025 * 2

i = 75

Answer from: Quest

Idon't take stuff like this new to me

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You know the right answer?

1.solve the equation. check for extraneous solutions.
|2z - 3| = 4z -1

2. solve ea...