Question

solve $|x + 5| = -7$
a. $x = -2$ and $x = -12$
b. $x = 2$ and $x = -12$
c. no solution
d. $x = -2$ and $x = 12$

Explanation:

Step1: Recall absolute value property

The absolute value of any real number, denoted as $|a|$, is always non-negative, meaning $|a| \geq 0$ for all real $a$.

Step2: Analyze the given equation

The equation is $|x+5| = -7$. Here, the right-hand side is $-7$, a negative number.

Step3: Compare with property

Since an absolute value cannot equal a negative number, there is no real number $x$ that satisfies the equation.

Answer:

C. No solution