Answer :

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]