Answer:
The values of x that satisfy the equation are -4 and -1.
Explanation:
To solve the equation (|5x+8|=3x), we can break it down into two separate equations based on the definition of the absolute value function.
When the expression inside the absolute value is positive or zero, the absolute value function can be removed.
When the expression inside the absolute value is negative, the absolute value function can be removed and the expression inside the absolute value is multiplied by -1.
So, we can solve the original equation as follows:
For (5x+8 = 3x):
[5x + 8 = 3x] Subtract 3x from both sides: [2x + 8 = 0]
Subtract 8 from both sides: [2x = -8]
Divide by 2: [x = -4]
For (5x+8 = -3x):
[5x + 8 = -3x] Add 3x to both sides: [8x + 8 = 0]
Subtract 8 from both sides: [8x = -8]
Divide by 8: [x = -1]
So, the solution to the equation (|5x+8|=3x) is:
[x = -4, -1]
Therefore, the values of x that satisfy the equation are -4 and -1.