Final answer:
To solve the equation 4|2y-7|+5=9, subtract 5, divide by 4, and consider the two cases for the absolute value resulting in two linear equations, which yield the solutions y=4 and y=3.
Step-by-step explanation:
The equation 4|2y-7|+5=9 can be solved by performing the following steps:
- Subtract 5 from both sides of the equation to isolate the absolute value expression on one side:
4|2y-7| = 4. - Divide both sides by 4 to simplify the equation:
|2y-7| = 1. - Recognize that an absolute value equation represents two possible scenarios - either the expression inside the absolute value is positive or negative. This gives us two separate equations to solve:
2y - 7 = 1 and 2y - 7 = -1. - Solve for y in both equations:
- For 2y - 7 = 1, add 7 to both sides: 2y = 8, and then divide by 2 to find y = 4.
- For 2y - 7 = -1, add 7 to both sides: 2y = 6, and then divide by 2 to find y = 3.
The solution to the original equation is y = 4 or y = 3.