The given equation has an ambiguity because it contains two equal signs. To address this, let's assume it was meant to be either of the following systems of equations:
1. [tex]\(-x - 5 = 4\)[/tex]
2. [tex]\(4 = -6\)[/tex]
First, let's analyze the first possible equation:
[tex]\[
-x - 5 = 4
\][/tex]
To solve for [tex]\(x\)[/tex], follow these steps:
1. Add 5 to both sides of the equation to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-x - 5 + 5 = 4 + 5
\][/tex]
[tex]\[
-x = 9
\][/tex]
2. Multiply both sides of the equation by [tex]\(-1\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
-x \cdot (-1) = 9 \cdot (-1)
\][/tex]
[tex]\[
x = -9
\][/tex]
Now, consider the second possible equation:
[tex]\[
4 = -6
\][/tex]
This statement is inherently false because [tex]\(4\)[/tex] is not equal to [tex]\(-6\)[/tex]. Consequently, this part of the equation does not contribute to a valid equation system.
Therefore, we should disregard any contradiction and focus on the most likely intended equation, which is:
[tex]\[
-x - 5 = -6
\][/tex]
Solve for [tex]\(x\)[/tex]:
1. Add 5 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-x - 5 + 5 = -6 + 5
\][/tex]
[tex]\[
-x = -1
\][/tex]
2. Multiply both sides by [tex]\(-1\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
-x \cdot (-1) = -1 \cdot (-1)
\][/tex]
[tex]\[
x = 1
\][/tex]
Thus, the solution to the equation is:
[tex]\[
x = 1
\][/tex]
