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Answer :
To simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex], we'll follow these steps:
1. Distribute the terms:
- For [tex]\(-9.2(8x - 4)\)[/tex], distribute [tex]\(-9.2\)[/tex] to both [tex]\(8x\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
-9.2 \times 8x = -73.6x
\][/tex]
[tex]\[
-9.2 \times (-4) = 36.8
\][/tex]
- For [tex]\(0.7(2 + 6.3x)\)[/tex], distribute [tex]\(0.7\)[/tex] to both [tex]\(2\)[/tex] and [tex]\(6.3x\)[/tex]:
[tex]\[
0.7 \times 2 = 1.4
\][/tex]
[tex]\[
0.7 \times 6.3x = 4.41x
\][/tex]
2. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-73.6x + 4.41x = -69.19x
\][/tex]
- Combine the constant terms:
[tex]\[
36.8 + 1.4 = 38.2
\][/tex]
3. Write the final simplified expression:
The simplified form of the expression is:
[tex]\[
-69.19x + 38.2
\][/tex]
Therefore, the correct answer is [tex]\(-69.19x + 38.2\)[/tex].
1. Distribute the terms:
- For [tex]\(-9.2(8x - 4)\)[/tex], distribute [tex]\(-9.2\)[/tex] to both [tex]\(8x\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
-9.2 \times 8x = -73.6x
\][/tex]
[tex]\[
-9.2 \times (-4) = 36.8
\][/tex]
- For [tex]\(0.7(2 + 6.3x)\)[/tex], distribute [tex]\(0.7\)[/tex] to both [tex]\(2\)[/tex] and [tex]\(6.3x\)[/tex]:
[tex]\[
0.7 \times 2 = 1.4
\][/tex]
[tex]\[
0.7 \times 6.3x = 4.41x
\][/tex]
2. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-73.6x + 4.41x = -69.19x
\][/tex]
- Combine the constant terms:
[tex]\[
36.8 + 1.4 = 38.2
\][/tex]
3. Write the final simplified expression:
The simplified form of the expression is:
[tex]\[
-69.19x + 38.2
\][/tex]
Therefore, the correct answer is [tex]\(-69.19x + 38.2\)[/tex].
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