Question

which of the following is(are) the solution(s) to $7|x + 2| = -49$? \
\
a. no solution \
\
b. all values are solutions \
\
c. $x = -5, 9$ \
\
d. $x = 5, -9$

Explanation:

Step1: Analyze the absolute value property

The absolute value of a number, denoted as \(|a|\), is always non - negative, i.e., \(|a|\geq0\) for any real number \(a\). In the equation \(7|x + 2|=-49\), first, we can divide both sides of the equation by 7.
\[
\frac{7|x + 2|}{7}=\frac{-49}{7}
\]

Step2: Simplify the equation

After simplifying the left - hand side and the right - hand side of the equation, we get \(|x + 2|=-7\). But we know that the absolute value of any real number \(x+2\) (where \(x\) is a real number) must be greater than or equal to 0. That is, \(|x + 2|\geq0\) for all real numbers \(x\), and \(-7<0\). So there is no real number \(x\) that can satisfy the equation \(|x + 2|=-7\).

Answer:

A. No Solution