College

What is [tex]-9.2(8x - 4) + 0.7(2 + 6.3x)[/tex] simplified?

A. [tex]-69.19x - 32.39[/tex]
B. [tex]-69.19x + 38.2[/tex]
C. [tex]-72.2x + 41.21[/tex]
D. [tex]75x - 338.2[/tex]

Answer :

Sure! Let's simplify the expression step by step:

Given expression:
[tex]\[ -9.2(8x - 4) + 0.7(2 + 6.3x) \][/tex]

1. Distribute [tex]\( -9.2 \)[/tex] and [tex]\( 0.7 \)[/tex] inside the parentheses:

[tex]\[
-9.2 \cdot (8x - 4) = -9.2 \cdot 8x + -9.2 \cdot (-4)
\][/tex]

[tex]\[
-9.2 \cdot 8x = -73.6x
\][/tex]

[tex]\[
-9.2 \cdot (-4) = 36.8
\][/tex]

So,

[tex]\[
-9.2(8x - 4) = -73.6x + 36.8
\][/tex]

Next,

[tex]\[
0.7 \cdot (2 + 6.3x) = 0.7 \cdot 2 + 0.7 \cdot 6.3x
\][/tex]

[tex]\[
0.7 \cdot 2 = 1.4
\][/tex]

[tex]\[
0.7 \cdot 6.3x = 4.41x
\][/tex]

So,

[tex]\[
0.7(2 + 6.3x) = 1.4 + 4.41x
\][/tex]

2. Combine the simplified parts:

[tex]\[
-73.6x + 36.8 + 1.4 + 4.41x
\][/tex]

3. Combine like terms [tex]\( x \)[/tex]-terms and constants:

[tex]\[
(-73.6x + 4.41x) + (36.8 + 1.4)
\][/tex]

[tex]\[
-69.19x + 38.2
\][/tex]

So, the simplified expression is:
[tex]\[ -69.19x + 38.2 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{-69.19x + 38.2} \][/tex]