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Answer :
To simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex], we'll proceed step by step:
1. Distribute [tex]\(-9.2\)[/tex] across the terms inside the first parenthesis:
- [tex]\(-9.2 \times 8x = -73.6x\)[/tex]
- [tex]\(-9.2 \times -4 = 36.8\)[/tex]
So, the expression becomes: [tex]\(-73.6x + 36.8\)[/tex].
2. Distribute [tex]\(0.7\)[/tex] across the terms inside the second parenthesis:
- [tex]\(0.7 \times 2 = 1.4\)[/tex]
- [tex]\(0.7 \times 6.3x = 4.41x\)[/tex]
So, the expression becomes: [tex]\(4.41x + 1.4\)[/tex].
3. Combine the results from both distributions:
The expression now is:
[tex]\[
-73.6x + 36.8 + 4.41x + 1.4
\][/tex]
4. 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]
5. Write the final simplified expression:
The simplified form of the original expression is:
[tex]\[
-69.19x + 38.2
\][/tex]
Therefore, the correct answer is [tex]\(-69.19x + 38.2\)[/tex].
1. Distribute [tex]\(-9.2\)[/tex] across the terms inside the first parenthesis:
- [tex]\(-9.2 \times 8x = -73.6x\)[/tex]
- [tex]\(-9.2 \times -4 = 36.8\)[/tex]
So, the expression becomes: [tex]\(-73.6x + 36.8\)[/tex].
2. Distribute [tex]\(0.7\)[/tex] across the terms inside the second parenthesis:
- [tex]\(0.7 \times 2 = 1.4\)[/tex]
- [tex]\(0.7 \times 6.3x = 4.41x\)[/tex]
So, the expression becomes: [tex]\(4.41x + 1.4\)[/tex].
3. Combine the results from both distributions:
The expression now is:
[tex]\[
-73.6x + 36.8 + 4.41x + 1.4
\][/tex]
4. 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]
5. Write the final simplified expression:
The simplified form of the original expression is:
[tex]\[
-69.19x + 38.2
\][/tex]
Therefore, the correct answer is [tex]\(-69.19x + 38.2\)[/tex].
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