Question

question

1. the equation $a = 4|x + 12| - 7$ has one solution for some value of $a$. solve for $a$.

answer attempt 1 out of 2

Explanation:

Step1: Recall absolute value properties

The absolute value expression $|x + 12|$ has a minimum value of $0$, since $|y| \geq 0$ for all real $y$.

Step2: Find minimum of the right-hand side

Substitute the minimum of $|x + 12|$ into the equation:
$$4(0) - 7 = -7$$

Step3: Verify one solution condition

When $a = -7$, the equation becomes $-7 = 4|x + 12| - 7$, which simplifies to $|x + 12| = 0$. This has exactly one solution: $x = -12$.

Answer:

$a = -7$