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Answer :
To simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex], let's go through it step by step:
1. Distribute [tex]\(-9.2\)[/tex] across the terms in the first set of parentheses:
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(8x\)[/tex] to get [tex]\(-73.6x\)[/tex].
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(-4\)[/tex] to get [tex]\(+36.8\)[/tex].
2. Distribute [tex]\(0.7\)[/tex] across the terms in the second set of parentheses:
- Multiply [tex]\(0.7\)[/tex] by [tex]\(2\)[/tex] to get [tex]\(+1.4\)[/tex].
- Multiply [tex]\(0.7\)[/tex] by [tex]\(6.3x\)[/tex] to get [tex]\(+4.41x\)[/tex].
Now, combine the like terms from both distributive results:
3. Combine the [tex]\(x\)[/tex] terms:
- [tex]\(-73.6x + 4.41x\)[/tex] gives [tex]\(-69.19x\)[/tex].
4. Combine the constant terms:
- [tex]\(+36.8 + 1.4\)[/tex] gives [tex]\(+38.2\)[/tex].
Therefore, the simplified expression is [tex]\(-69.19x + 38.2\)[/tex].
So, the correct answer is [tex]\(-69.19x + 38.2\)[/tex].
1. Distribute [tex]\(-9.2\)[/tex] across the terms in the first set of parentheses:
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(8x\)[/tex] to get [tex]\(-73.6x\)[/tex].
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(-4\)[/tex] to get [tex]\(+36.8\)[/tex].
2. Distribute [tex]\(0.7\)[/tex] across the terms in the second set of parentheses:
- Multiply [tex]\(0.7\)[/tex] by [tex]\(2\)[/tex] to get [tex]\(+1.4\)[/tex].
- Multiply [tex]\(0.7\)[/tex] by [tex]\(6.3x\)[/tex] to get [tex]\(+4.41x\)[/tex].
Now, combine the like terms from both distributive results:
3. Combine the [tex]\(x\)[/tex] terms:
- [tex]\(-73.6x + 4.41x\)[/tex] gives [tex]\(-69.19x\)[/tex].
4. Combine the constant terms:
- [tex]\(+36.8 + 1.4\)[/tex] gives [tex]\(+38.2\)[/tex].
Therefore, the simplified expression is [tex]\(-69.19x + 38.2\)[/tex].
So, the correct answer is [tex]\(-69.19x + 38.2\)[/tex].
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