High School

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]

Step 1: Distribute -9.2 across the terms inside the first parenthesis.

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

Step 2: Distribute 0.7 across the terms inside the second parenthesis.

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

Step 3: Combine all the terms.

Now, combine the [tex]\(x\)[/tex] terms and the constant terms:

- 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]

So, the simplified expression is:

[tex]\[ -69.19x + 38.2 \][/tex]

The correct answer is:

[tex]\[ -69.19x + 38.2 \][/tex]

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