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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 :

Sure! Let's simplify the expression step-by-step:

We start with the expression:
[tex]\[
-9.2(8x - 4) + 0.7(2 + 6.3x)
\][/tex]

1. Distribute the [tex]\(-9.2\)[/tex] in the first part:
- 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, [tex]\(-9.2(8x - 4)\)[/tex] simplifies to:
[tex]\(-73.6x + 36.8\)[/tex]

2. Distribute the [tex]\(0.7\)[/tex] in the second part:
- Multiply [tex]\(0.7\)[/tex] by [tex]\(6.3x\)[/tex]: [tex]\(0.7 \times 6.3x = 4.41x\)[/tex]
- Multiply [tex]\(0.7\)[/tex] by [tex]\(2\)[/tex]: [tex]\(0.7 \times 2 = 1.4\)[/tex]

So, [tex]\(0.7(2 + 6.3x)\)[/tex] simplifies to:
[tex]\(1.4 + 4.41x\)[/tex]

3. 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]

Putting it all together, the expression simplifies to:
[tex]\[
-69.19x + 38.2
\][/tex]

Therefore, the simplified expression is:
[tex]\[
-69.19x + 38.2
\][/tex]

This matches one of the given answer options:
[tex]\[
-69.19x + 38.2
\][/tex]

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