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]
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]
