Final answer:
To solve the equation 4 = 4|x + 4| + 7, subtract 7 from both sides and divide by 4. Split the equation into two cases by considering the absolute value expression as both positive and negative. Solve for x in each case to find the solutions.
Step-by-step explanation:
Solving the equation:
4 = 4|x + 4| + 7
First, subtract 7 from both sides to isolate the absolute value expression: 4 - 7 = 4|x + 4|
Simplify the left side: -3 = 4|x + 4|
Divide both sides by 4: -3/4 = |x + 4|
Now, we have two possible cases to consider:
Case 1: |x + 4| = -3/4 (not valid because absolute value cannot be negative)
Case 2: |x + 4| = 3/4
Now split the equation into two separate cases:
Case 2.1: x + 4 = 3/4
Solve for x: x = 3/4 - 4
Simplify: x = -13/4
Case 2.2: x + 4 = -3/4
Solve for x: x = -3/4 - 4
Simplify: x = -19/4
Therefore, the solutions are x = -13/4 and x = -19/4.