Question
Given the function \( f(x)=-5|x+1|+3 \), for what values of \( x \) is \( f(x)=-12 ? \) \( x=-2, x=-4 \) \( x=-2, x=4 \) \( x=2, x=-4 \) \( x=2, x=4 \)
Ask by Schultz Johnston. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The values of \( x \) that satisfy \( f(x) = -12 \) are \( x = 2 \) and \( x = -4 \).
Solution
To solve f(x) = -12 for the function f(x) = -5|x + 1| + 3, follow these steps:
1. Set the function equal to -12:
-5|x + 1| + 3 = -12
2. Subtract 3 from both sides:
-5|x + 1| = -15
3. Divide both sides by -5:
|x + 1| = 3
4. Solve the absolute value equation:
x + 1 = 3 or x + 1 = -3
Case 1:
x + 1 = 3 ⟹ x = 2
Case 2:
x + 1 = -3 ⟹ x = -4
So the values of x for which f(x) = -12 are x = 2 and x = -4.
The correct answer among the options is: x = 2, x = -4.
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Simplify this solution The Deep Dive
To find the values of \( x \) for which \( f(x) = -12 \), we start with the function \( f(x) = -5|x+1| + 3 \). Setting this equal to -12 gives us the equation: \[ -5|x+1| + 3 = -12 \] Subtracting 3 from both sides results in: \[ -5|x+1| = -15 \] Dividing both sides by -5, we find: \[ |x+1| = 3 \] The absolute value results in two cases: 1. \( x + 1 = 3 \) which simplifies to \( x = 2 \) 2. \( x + 1 = -3 \) which simplifies to \( x = -4 \) Therefore, the values of \( x \) are \( x = 2 \) and \( x = -4 \). So, the correct answer is \( x=2, x=-4 \).
