Certainly! Let's break down the expression step-by-step given [tex]\( x = 4 \)[/tex], [tex]\( y = 3 \)[/tex], and [tex]\( z = -2 \)[/tex].
We are asked to evaluate the expression [tex]\( x - 2y + 3z \)[/tex].
1. Substituting the values:
[tex]\[
x = 4, \quad y = 3, \quad z = -2
\][/tex]
2. Substitute these values into the expression:
[tex]\[
x - 2y + 3z = 4 - 2(3) + 3(-2)
\][/tex]
3. Perform the multiplication within the expression:
[tex]\[
4 - 2 \cdot 3 + 3 \cdot (-2)
\][/tex]
[tex]\[
4 - 6 + (-6)
\][/tex]
4. Simplify step-by-step:
[tex]\[
4 - 6 = -2
\][/tex]
[tex]\[
-2 + (-6) = -8
\][/tex]
So, the result of the expression [tex]\( x - 2y + 3z \)[/tex] when [tex]\( x = 4 \)[/tex], [tex]\( y = 3 \)[/tex], and [tex]\( z = -2 \)[/tex] is:
[tex]\[
\boxed{-8}
\][/tex]
