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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 [tex]\(-9.2\)[/tex] in the term [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]
- Therefore, [tex]\(-9.2(8x - 4)\)[/tex] simplifies to:
[tex]\[
-73.6x + 36.8
\][/tex]

2. Distribute [tex]\(0.7\)[/tex] in the term [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]
- Therefore, [tex]\(0.7(2 + 6.3x)\)[/tex] simplifies to:
[tex]\[
1.4 + 4.41x
\][/tex]

3. Combine like terms from both expressions:
- 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]

4. Final simplified expression:
[tex]\[
-69.19x + 38.2
\][/tex]

So, the simplified expression is [tex]\(-69.19x + 38.2\)[/tex], which matches the choice [tex]\(-69.19x + 38.2\)[/tex].

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Rewritten by : Jeany

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