Solve the absolute value equation 4x-1=1 answers are. X=2 or x=0,, x=0or x=-1/2, x=0or x=1/2, x=2 Oryx=-1/2
If you mean
|4x-1| = 1
then you need to recall that
|n| = n if n>=0
|n| = -n if n<0
So, we have two cases, which must be solved separately
4x-1 >= 0
4x-1=1
4x=2 x = 1/2
Since x=1/2 satisfies the condition that 4x-1 >= 0, it is a solution
4x-1 < 0
-(4x-1) = 1
-4x+1=1
-4x=0-
x=0
Since x=0 satisfies the condition that 4x-1<0, x=0 is another solution.
So, x = 0 or 1/2
This seems reasonable, since you know that |4x-1| has a v-shaped graph, which will likely intersect a horizontal line in two points.
To see this, visit
http://www.wolframalpha.com/input/?i=solve+|4x-1|%3D1
Note also that we could recognize that (x)^2 = x^2 and (-x)^2 = x^2, so we could write
(4x-1)^2 = 1^2
16x^2-8x+1=1
16x^2-8x=0
8x(2x-1) = 0
x=0 or 1/2
To solve the absolute value equation 4x-1=1, you need to break it into two separate cases: one where the expression inside the absolute value is positive, and one where it is negative.
Case 1: 4x-1 > 0
Add 1 to both sides of the equation:
4x > 2
Divide both sides by 4:
x > 1/2
Case 2: 4x-1 < 0
Add 1 to both sides of the equation:
4x < 2
Divide both sides by 4:
x < 1/2
So, the solutions for the absolute value equation 4x-1=1 are:
x > 1/2 or x < 1/2
However, let's check the values to see if they satisfy the original equation:
For x > 1/2:
Let's choose x = 2:
4(2) - 1 = 8 - 1 = 7 (not equal to 1)
For x < 1/2:
Let's choose x = 0:
4(0) - 1 = -1 (not equal to 1)
Therefore, neither x > 1/2 nor x < 1/2 satisfies the equation.
Hence, there are no solutions for the given absolute value equation.
To solve the absolute value equation 4x - 1 = 1, we can follow these steps:
Step 1: Isolate the absolute value expression on one side of the equation.
Subtract 1 from both sides:
4x - 1 - 1 = 1 - 1
4x - 2 = 0
Step 2: Set up two separate equations, one for when the absolute value is positive and one for when it is negative.
4x - 2 = 0 (when the absolute value is positive)
-(4x - 2) = 0 (when the absolute value is negative)
Step 3: Solve each equation separately.
For the equation 4x - 2 = 0:
Add 2 to both sides:
4x - 2 + 2 = 0 + 2
4x = 2
Divide both sides by 4:
4x/4 = 2/4
x = 1/2
For the equation -(4x - 2) = 0:
Multiply both sides by -1 to change the sign:
-1 * -(4x - 2) = 0 * -1
4x - 2 = 0
Follow the steps we used in the previous equation to solve it:
4x - 2 + 2 = 0 + 2
4x = 2
4x/4 = 2/4
x = 1/2
So, the solutions to the absolute value equation 4x - 1 = 1 are x = 1/2 and x = 1/2.