To determine the values for which the expression [tex]\(\frac{8}{-6x - 3}\)[/tex] is undefined, we need to identify when the denominator is equal to zero. This is because division by zero is undefined in mathematics.
Let's set the denominator [tex]\(-6x - 3\)[/tex] equal to zero and solve for [tex]\(x\)[/tex]:
[tex]\[
-6x - 3 = 0
\][/tex]
First, add 3 to both sides of the equation:
[tex]\[
-6x - 3 + 3 = 0 + 3 \implies -6x = 3
\][/tex]
Next, divide both sides by -6:
[tex]\[
x = \frac{3}{-6}
\][/tex]
Simplify the fraction:
[tex]\[
x = -\frac{1}{2}
\][/tex]
Therefore, the value that makes the denominator zero and thus makes the expression undefined is:
[tex]\[
x = -\frac{1}{2}
\][/tex]
So, the excluded value for the expression [tex]\(\frac{8}{-6x - 3}\)[/tex] is:
[tex]\[
x = -\frac{1}{2}
\][/tex]
