To find the limit of the expression [tex]\(2x + 3x - 14\)[/tex] as [tex]\(x\)[/tex] approaches 2, we can follow these steps:
1. Simplify the expression:
Let's combine like terms in the expression [tex]\(2x + 3x - 14\)[/tex].
[tex]\[
2x + 3x = 5x
\][/tex]
So, the expression simplifies to:
[tex]\[
5x - 14
\][/tex]
2. Substitute the value of [tex]\(x\)[/tex]:
Now we need to find the limit as [tex]\(x\)[/tex] approaches 2. We substitute [tex]\(x = 2\)[/tex] into the simplified expression [tex]\(5x - 14\)[/tex]:
[tex]\[
5(2) - 14
\][/tex]
3. Evaluate the expression:
Perform the multiplication and subtraction:
[tex]\[
5 \cdot 2 = 10
\][/tex]
[tex]\[
10 - 14 = -4
\][/tex]
Thus, the limit of the expression [tex]\(2x + 3x - 14\)[/tex] as [tex]\(x\)[/tex] approaches 2 is:
[tex]\[
\boxed{-4}
\][/tex]
