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Answer :
Let's simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] step by step:
1. Distribute [tex]\(-9.2\)[/tex] into the first parentheses [tex]\((8x - 4)\)[/tex]:
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(8x\)[/tex]: [tex]\(-9.2 \times 8x = -73.6x\)[/tex]
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(-4\)[/tex]: [tex]\(-9.2 \times -4 = 36.8\)[/tex]
- So, the result from distributing [tex]\(-9.2\)[/tex] is: [tex]\(-73.6x + 36.8\)[/tex]
2. Distribute [tex]\(0.7\)[/tex] into the second parentheses [tex]\((2 + 6.3x)\)[/tex]:
- Multiply [tex]\(0.7\)[/tex] by [tex]\(2\)[/tex]: [tex]\(0.7 \times 2 = 1.4\)[/tex]
- Multiply [tex]\(0.7\)[/tex] by [tex]\(6.3x\)[/tex]: [tex]\(0.7 \times 6.3x = 4.41x\)[/tex]
- So, the result from distributing [tex]\(0.7\)[/tex] is: [tex]\(1.4 + 4.41x\)[/tex]
3. Combine the results from both distributions:
- Combine the like terms (terms with [tex]\(x\)[/tex]): [tex]\(-73.6x + 4.41x = -69.19x\)[/tex]
- Combine the constant terms: [tex]\(36.8 + 1.4 = 38.2\)[/tex]
4. Write the simplified expression:
- The simplified expression is: [tex]\(-69.19x + 38.2\)[/tex]
Therefore, the simplified form of the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] is [tex]\(-69.19x + 38.2\)[/tex].
The correct choice from the given options is: [tex]\(-69.19x + 38.2\)[/tex].
1. Distribute [tex]\(-9.2\)[/tex] into the first parentheses [tex]\((8x - 4)\)[/tex]:
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(8x\)[/tex]: [tex]\(-9.2 \times 8x = -73.6x\)[/tex]
- Multiply [tex]\(-9.2\)[/tex] by [tex]\(-4\)[/tex]: [tex]\(-9.2 \times -4 = 36.8\)[/tex]
- So, the result from distributing [tex]\(-9.2\)[/tex] is: [tex]\(-73.6x + 36.8\)[/tex]
2. Distribute [tex]\(0.7\)[/tex] into the second parentheses [tex]\((2 + 6.3x)\)[/tex]:
- Multiply [tex]\(0.7\)[/tex] by [tex]\(2\)[/tex]: [tex]\(0.7 \times 2 = 1.4\)[/tex]
- Multiply [tex]\(0.7\)[/tex] by [tex]\(6.3x\)[/tex]: [tex]\(0.7 \times 6.3x = 4.41x\)[/tex]
- So, the result from distributing [tex]\(0.7\)[/tex] is: [tex]\(1.4 + 4.41x\)[/tex]
3. Combine the results from both distributions:
- Combine the like terms (terms with [tex]\(x\)[/tex]): [tex]\(-73.6x + 4.41x = -69.19x\)[/tex]
- Combine the constant terms: [tex]\(36.8 + 1.4 = 38.2\)[/tex]
4. Write the simplified expression:
- The simplified expression is: [tex]\(-69.19x + 38.2\)[/tex]
Therefore, the simplified form of the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] is [tex]\(-69.19x + 38.2\)[/tex].
The correct choice from the given options is: [tex]\(-69.19x + 38.2\)[/tex].
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