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Answer :
To simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex], we will distribute the numbers and then combine like terms. Let's break it down step by step.
1. Distribute [tex]\(-9.2\)[/tex] over [tex]\((8x - 4)\)[/tex]:
- First, multiply [tex]\(-9.2\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
-9.2 \times 8x = -73.6x
\][/tex]
- Next, multiply [tex]\(-9.2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
-9.2 \times (-4) = 36.8
\][/tex]
So, the distribution results in [tex]\(-73.6x + 36.8\)[/tex].
2. Distribute [tex]\(0.7\)[/tex] over [tex]\((2 + 6.3x)\)[/tex]:
- First, multiply [tex]\(0.7\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
0.7 \times 2 = 1.4
\][/tex]
- Next, multiply [tex]\(0.7\)[/tex] by [tex]\(6.3x\)[/tex]:
[tex]\[
0.7 \times 6.3x = 4.41x
\][/tex]
So, the distribution results in [tex]\(1.4 + 4.41x\)[/tex].
3. Combine like terms:
- For the x terms: Add [tex]\(-73.6x\)[/tex] and [tex]\(4.41x\)[/tex]:
[tex]\[
-73.6x + 4.41x = -69.19x
\][/tex]
- For the constant terms: Add [tex]\(36.8\)[/tex] and [tex]\(1.4\)[/tex]:
[tex]\[
36.8 + 1.4 = 38.2
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
-69.19x + 38.2
\][/tex]
This means the correct choice among the given options is [tex]\(-69.19x + 38.2\)[/tex].
1. Distribute [tex]\(-9.2\)[/tex] over [tex]\((8x - 4)\)[/tex]:
- First, multiply [tex]\(-9.2\)[/tex] by [tex]\(8x\)[/tex]:
[tex]\[
-9.2 \times 8x = -73.6x
\][/tex]
- Next, multiply [tex]\(-9.2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
-9.2 \times (-4) = 36.8
\][/tex]
So, the distribution results in [tex]\(-73.6x + 36.8\)[/tex].
2. Distribute [tex]\(0.7\)[/tex] over [tex]\((2 + 6.3x)\)[/tex]:
- First, multiply [tex]\(0.7\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
0.7 \times 2 = 1.4
\][/tex]
- Next, multiply [tex]\(0.7\)[/tex] by [tex]\(6.3x\)[/tex]:
[tex]\[
0.7 \times 6.3x = 4.41x
\][/tex]
So, the distribution results in [tex]\(1.4 + 4.41x\)[/tex].
3. Combine like terms:
- For the x terms: Add [tex]\(-73.6x\)[/tex] and [tex]\(4.41x\)[/tex]:
[tex]\[
-73.6x + 4.41x = -69.19x
\][/tex]
- For the constant terms: Add [tex]\(36.8\)[/tex] and [tex]\(1.4\)[/tex]:
[tex]\[
36.8 + 1.4 = 38.2
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
-69.19x + 38.2
\][/tex]
This means the correct choice among the given options is [tex]\(-69.19x + 38.2\)[/tex].
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