Final answer:
To solve the absolute value equations, break each into two cases: one where the value inside is positive, and one where it's negative. Solve the resulting equations, simplify the algebra, and check if the answers are reasonable.
Step-by-step explanation:
The student's question involves solving equations with absolute values. Solving such equations requires considering both the positive and the negative scenarios that the absolute value could represent. For each equation, we will split the problem into two separate cases based on the definition of absolute value.
Equation a: |4b-5|=19
Case 1: 4b - 5 = 19
Case 2: 4b - 5 = -19
Solve both cases separately to find the possible values for b.
Equation c: 3=-2|1/4s-5|+3
Rearrange the equation to isolate the absolute value part:
-2|1/4s-5|=0
Then solve for s, considering both the positive and negative scenarios.
Equation d: |4n-15|=|n|
Set up two pairs of equations based on the absolute values:
Case 1: 4n - 15 = n
Case 2: 4n - 15 = -n
Solve both cases to find the possible values for n.
Throughout the process, eliminate terms wherever possible to simplify the algebra. After finding the solutions, check if the answers are reasonable in context.