Question

solve |x + 4| = -7
a. x = 3 and x = -11
b. x = -3 and x = 11
c. x = -3 and x = -11
d. no solution

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 $|x+4| = -7$. 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:

D. No solution