Solve the equation. |4x-1|=7

Edmund Adams

Edmund Adams

Answered question

2021-11-17

Solve the equation.
|4x1|=7

Answer & Explanation

Michele Grimsley

Michele Grimsley

Beginner2021-11-18Added 19 answers

Step 1
Module(absolute value) of a positive number or zero is the number itself and module of a negative number is called its contrary number i.e.
|a|=aifa0
and
|a|=-a if a<0
From |4x-1|=7 we get that 4x−1=7 and 4x−1=−7
Step 2
From the first equation we find
4x-1=7
4x=7+1
4x=8
x=2
and from the second
4x-1=-7
4x=-7+1
4x=-6
x=32
Philip O'Neill

Philip O'Neill

Beginner2021-11-19Added 8 answers

Step 1: Rearrange this Absolute Value Equation
Absolute value equalitiy entered
|4x-1| = 7
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 |4x-1|
For the Negative case we'll use -(4x-1)
For the Positive case we'll use (4x-1)
Step 3: Solve the Negative Case
-(4x-1) = 7
Multiply
-4x+1 = 7
Rearrange and Add up
-4x = 6
Divide both sides by 4
-x = (3/2)
Multiply both sides by (-1)
x = -(3/2)
Which is the solution for the Negative Case
Step 4: Solve the Positive Case
(4x-1) = 7
Rearrange and Add up
4x = 8
Divide both sides by 4
x = 2
Which is the solution for the Positive Case
Step 5: rap up the solution
x=-3/2
x=2

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