To simplify the expression [tex]\( 2(4x + 7) - 3(2x - 4) \)[/tex], we need to follow a few algebraic steps. Let's break it down step-by-step.
1. Distribute the 2 in the first term [tex]\( 2(4x + 7) \)[/tex]:
[tex]\[
2(4x + 7) = 2 \cdot 4x + 2 \cdot 7 = 8x + 14
\][/tex]
2. Distribute the 3 in the second term [tex]\( -3(2x - 4) \)[/tex]:
[tex]\[
-3(2x - 4) = -3 \cdot 2x + (-3) \cdot (-4) = -6x + 12
\][/tex]
3. Combine the distributed terms:
The original expression is now:
[tex]\[
8x + 14 - 6x + 12
\][/tex]
4. Combine like terms:
Group the [tex]\( x \)[/tex] terms and constant terms together:
[tex]\[
(8x - 6x) + (14 + 12)
\][/tex]
Simplify the grouped terms:
[tex]\[
2x + 26
\][/tex]
So, the simplified expression for [tex]\( 2(4x + 7) - 3(2x - 4) \)[/tex] is [tex]\( 2x + 26 \)[/tex].
Thus, the correct answer is [tex]\( 2x + 26 \)[/tex].
