Final answer:
In solving the equation 2|3x-4|+8=6, we find that after isolating the absolute value term, it equates to -2, which is not possible as absolute values cannot be negative. Therefore, the equation has no solution.
Step-by-step explanation:
To solve the equation 2|3x-4|+8=6, we need to follow these steps:
- First, subtract 8 from both sides of the equation to isolate the absolute value term:
- Since the absolute value of any number is always non-negative, there are no solutions to this equation when the absolute value is set equal to a negative number. Therefore, the equation 2|3x-4|+8=6 has no solution.
It's important to eliminate terms wherever possible to simplify the algebra. We also need to check the answer to see if it is reasonable. In this case, since the absolute value cannot result in a negative number when multiplied by a positive number, we know that it is reasonable to conclude that there are no solutions to this equation.
Solving absolute value equations involves finding the values of the variable that satisfy the equation, considering the distance of the variable from zero on the number line. For an equation like |x - a| = b, where 'a' is a constant and 'b' is a positive value, solutions can be obtained by considering both positive and negative values that make the expression inside the absolute value equal to 'b'. Depending on the context, there may be one, two, or no solutions. Understanding the absolute value concept is crucial for solving equations involving distances and ranges, often encountered in algebra and real-world applications.