2|3x-5|-8=8
2(3x-5)= 16
6x -10 = 16
6 x = 26
x = 13/3
and
2(-3x+5) =16
-6x + 10 = 16
6 x = -6
x = -1
or, look at it like this:
2|3x-5|-8=8
2|3x-5| = 16
|3x-5| = 8
|x - 5/3| = 8/3
so, x = 5/3 ± 8/3
x = 13/3 or -1
or, you can use the "extraneous root" introduced by squaring both sides.
|3x-5| = 8
(3x-5)^2 = 64
3x-5 = ±8
3x = 5±8
x = 5/3 ± 8/3
To solve the equation 2|3x-5|-8=8, we will need to follow these steps:
Step 1: Remove the absolute value bars
To remove the absolute value bars, we need to consider two cases:
1. When 3x-5 is positive:
In this case, we can simply remove the absolute value bars without changing the expression. So the equation becomes:
2(3x-5) - 8 = 8
2. When 3x-5 is negative:
In this case, we need to change the sign of the expression inside the absolute value bars. So the equation becomes:
2(-(3x-5)) - 8 = 8
Simplifying this, we get: -6x + 10 - 8 = 8
Which simplifies further to: -6x + 2 = 8
Step 2: Solve the resulting linear equations
Now, we solve each case separately.
Case 1: 2(3x-5) - 8 = 8
Distribute 2, and then isolate the variable term:
6x - 10 - 8 = 8
6x - 18 = 8
Add 18 to both sides:
6x = 26
Divide both sides by 6:
x = 26/6
Simplifying this, we get:
x = 13/3
Case 2: -6x + 2 = 8
Isolate the variable term:
-6x = 8 - 2
-6x = 6
Divide both sides by -6 (to solve for x):
x = 6/-6
Simplifying this, we get:
x = -1
So the solution to the equation 2|3x-5|-8=8 is x = 13/3 or x = -1.