Question

Solve each absolute value equation, write the solution in set notation.

5.3|q + 9.2| + 6.7 = 43.8

A) { -16.7, 1.5 }
B) { 4.2, -18.4 }
C) { -7.9, 8.3 }
D) { 10.6, -20.4 }

Answer 1

The absolute value equation is solved by isolating the absolute value expression and considering both cases where the expression inside the absolute value is equal to 7 and -7. However, the solutions found do not match the provided answer choices, suggesting a mistake in the question or calculations.

Step-by-step explanation:

To solve the absolute value equation 5.3|q + 9.2| + 6.7 = 43.8, we first isolate the absolute value expression by subtracting 6.7 from both sides:

5.3|q + 9.2| = 43.8 - 6.7
5.3|q + 9.2| = 37.1

Next, we divide by 5.3 to get the absolute value by itself:

|q + 9.2| = 37.1 / 5.3
|q + 9.2| = 7

Now, we consider the two cases for the absolute value to be 7:

1. q + 9.2 = 7
2. q + 9.2 = -7

Solving each case:

1. q = 7 - 9.2
   q = -2.2
2. q = -7 - 9.2
   q = -16.2

However, neither solution matches any of the options provided, indicating a potential typo or mistake in either the provided equation or the answer choices. In a real-world scenario, we would need to recheck the original problem or the calculations to ensure accuracy.