Great question! Let's verify that the expression [tex]$3(4x - 6)$[/tex] simplifies to [tex]$12x - 18$[/tex] by evaluating both expressions when [tex]$x = 2$[/tex]. Here's a step-by-step solution:
### Step-by-Step Solution:
1. Evaluate the first expression [tex]$3(4x - 6)$[/tex] for [tex]$x = 2$[/tex]:
- First, substitute [tex]$x = 2$[/tex] into the expression:
[tex]\[
3(4 \cdot 2 - 6)
\][/tex]
- Perform the multiplication inside the parentheses:
[tex]\[
3(8 - 6)
\][/tex]
- Simplify inside the parentheses:
[tex]\[
3 \cdot 2
\][/tex]
- Finally, perform the multiplication:
[tex]\[
6
\][/tex]
2. Evaluate the second expression [tex]$12x - 18$[/tex] for [tex]$x = 2$[/tex]:
- Substitute [tex]$x = 2$[/tex] into the expression:
[tex]\[
12 \cdot 2 - 18
\][/tex]
- Perform the multiplication:
[tex]\[
24 - 18
\][/tex]
- Simplify the result:
[tex]\[
6
\][/tex]
### Conclusion
When [tex]$x = 2$[/tex], both expressions [tex]$3(4x - 6)$[/tex] and [tex]$12x - 18$[/tex] evaluate to [tex]$6$[/tex]. Therefore, the value of each expression when substituting [tex]$x = 2$[/tex] is indeed 6.
Therefore, the correct option is:
"The value of each expression is 6."
