|(2x-5)/3| = |(3x+4)/2|
Case 1:
(2x-5)/3 = (3x+4)/2
9x+12 = 4x - 10
5x = -22
x = -22/5
case 2:
(2x-5)/3 = -(3x+4)/2
4x - 10 = -9x -12
13x = -2
x = -2/13
Can u explain in words how to do that because I still do not get it using numbers
To solve the absolute value equation |(2x-5)/3| = |(3x+4)/2|, we can approach it in two parts:
PART 1: (2x-5)/3 = (3x+4)/2
First, we can eliminate the denominators by multiplying both sides of the equation by 6:
6 * (2x-5)/3 = 6 * (3x+4)/2
2(2x-5) = 3(3x+4)
4x - 10 = 9x + 12
Now, we can solve for x:
4x - 9x = 12 + 10 (adding 9x to both sides and adding 10 to both sides)
-5x = 22
x = -22/5
PART 2: (2x-5)/3 = -(3x+4)/2
Next, we can set up the equation with the opposite sign for the right side:
(2x-5)/3 = -(3x+4)/2
To eliminate the denominators, we can multiply both sides of the equation by 6:
6 * (2x-5)/3 = 6 * -(3x+4)/2
2(2x-5) = -3(3x+4)
4x - 10 = -9x - 12
Now, we can solve for x:
4x + 9x = -12 + 10 (adding 9x to both sides and adding 10 to both sides)
13x = -2
x = -2/13
So the solution to the absolute value equation |(2x-5)/3| = |(3x+4)/2| is x = -22/5 or x = -2/13.