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What is [tex]-9.2(8x - 4) + 0.7(2 + 6.3x)[/tex] simplified?

A. [tex]-69.19x - 32.39[/tex]

B. [tex]-69.19x + 38.2[/tex]

C. [tex]-72.2x + 41.21[/tex]

D. [tex]75x - 338.2[/tex]

Answer :

Let's simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] step by step:

1. Distribute in the first part [tex]\(-9.2(8x - 4)\)[/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]

The expression becomes: [tex]\(-73.6x + 36.8\)[/tex]

2. Distribute in the second part [tex]\(0.7(2 + 6.3x)\)[/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]

The expression becomes: [tex]\(1.4 + 4.41x\)[/tex]

3. Combine the expressions:
- Combine the terms from both parts: [tex]\(-73.6x + 36.8 + 1.4 + 4.41x\)[/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]

The simplified expression is [tex]\(-69.19x + 38.2\)[/tex].

Therefore, the correct answer is [tex]\(-69.19x + 38.2\)[/tex].

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