Solve |5x-2| = |5x+4|
To solve |5x-2| = |5x+4|, we can square both sides of the equation to eliminate the absolute value symbols.
(5x-2)^2 = (5x+4)^2
Expanding both sides, we get:
25x^2 - 20x + 4 = 25x^2 + 40x + 16
Combining like terms and simplifying, we have:
-20x + 4 = 40x + 16
Subtract 40x from both sides:
-60x + 4 = 16
Subtract 4 from both sides:
-60x = 12
Divide both sides by -60:
x = -12/60
Simplifying the fraction, we get:
x = -1/5
Therefore, the solution to the equation |5x-2| = |5x+4| is x = -1/5.
To solve the equation |5x-2| = |5x+4|, we'll need to consider two cases: when the expression inside the absolute value bars is positive and when it is negative.
Case 1: When 5x - 2 is positive (5x - 2 > 0)
In this case, we can remove the absolute value symbols without changing the equation.
So, we have 5x - 2 = 5x + 4.
Subtracting 5x from both sides, we get:
-2 = 4.
Since -2 is not equal to 4, this case does not yield a valid solution. So, let's move on to the second case.
Case 2: When 5x - 2 is negative (5x - 2 < 0)
In this case, we need to flip the inequality sign when removing the absolute value symbols.
So, we have -(5x - 2) = 5x + 4.
Distributing the negative sign, we get:
-5x + 2 = 5x + 4.
Now, let's solve for x:
Subtracting 2 from both sides, we get:
-5x = 5x + 2.
Adding 5x to both sides, we get:
0 = 10x + 2.
Subtracting 2 from both sides, we get:
-2 = 10x.
Dividing both sides by 10, we get:
x = -2/10.
Simplifying the fraction, we have:
x = -1/5.
Therefore, the solution to the equation |5x-2| = |5x+4| is x = -1/5.
To solve the equation |5x-2| = |5x+4|, we'll need to consider two cases - one where the expressions inside the absolute value are positive, and another where they are negative.
Case 1: If 5x - 2 is positive, and 5x + 4 is positive:
In this case, the equation simplifies to (5x - 2) = (5x + 4). To solve for x, we can isolate the variable by subtracting 5x from both sides:
5x - 5x - 2 = 5x - 5x + 4
-2 = 4
This equation is not true, which means there are no solutions in this case.
Case 2: If 5x - 2 is negative, and 5x + 4 is negative:
In this case, the equation becomes -(5x - 2) = -(5x + 4). The negative sign on each side is necessary because we are dealing with negative numbers inside the absolute value.
Distributing the negative sign, we get -5x + 2 = -5x - 4. Simplifying further, we subtract -5x from both sides to isolate the variable:
-5x + 5x + 2 = -5x - 5x - 4
2 = -4
Again, this equation is not true, which means there are no solutions in this case either.
Since there are no solutions in either case, the original equation |5x-2| = |5x+4| does not have any solutions.