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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 [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] step-by-step.

1. Distribute the -9.2:
- Multiply [tex]\(-9.2\)[/tex] by each term inside the parentheses:
[tex]\[
-9.2 \times 8x = -73.6x
\][/tex]
[tex]\[
-9.2 \times -4 = 36.8
\][/tex]

So, [tex]\(-9.2(8x - 4)\)[/tex] becomes [tex]\(-73.6x + 36.8\)[/tex].

2. Distribute the 0.7:
- Multiply [tex]\(0.7\)[/tex] by each term inside the parentheses:
[tex]\[
0.7 \times 2 = 1.4
\][/tex]
[tex]\[
0.7 \times 6.3x = 4.41x
\][/tex]

So, [tex]\(0.7(2 + 6.3x)\)[/tex] becomes [tex]\(1.4 + 4.41x\)[/tex].

3. Combine like terms from both distributions:
- For the [tex]\(x\)[/tex] terms:
[tex]\[
-73.6x + 4.41x = -69.19x
\][/tex]

- For the constant terms:
[tex]\[
36.8 + 1.4 = 38.2
\][/tex]

4. Put it all together:
[tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] simplifies to:
[tex]\[
-69.19x + 38.2
\][/tex]

Therefore, the simplified form of the given expression is [tex]\(-69.19x + 38.2\)[/tex], so the correct answer is:
[tex]\[
-69.19x + 38.2
\][/tex]

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