Final answer:
To solve |4x+5| = |-29+4x|, we consider two cases. The first case leads to no solution, while the second case, after simplifying, gives the solution x = 3.
Step-by-step explanation:
To solve the equation |4x+5| = |-29+4x|, we need to consider two cases based on the properties of absolute value:
Case 1: 4x + 5 = -29 + 4x
If the expressions inside the absolute values are equal, the absolute values will also be equal. In this case, we can subtract 4x from both sides, which simplifies to 5 = -29 which is not possible. Hence, there is no solution in this case.
Case 2: 4x + 5 = 29 - 4x
This case assumes that one absolute value is the negative of the other. To solve for x, we combine like terms by adding 4x to both sides, obtaining 8x + 5 = 29. Subtracting 5 from both sides, we get 8x = 24, and by dividing both sides by 8, we find that x = 3.
In summary, the solution to the equation is x = 3.