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 :

To simplify the expression [tex]-9.2(8x - 4) + 0.7(2 + 6.3x)[/tex], follow these steps:

  1. Distribute the terms inside the parentheses:

    • Multiply [tex]-9.2[/tex] by each term inside the first parentheses:
      [tex]-9.2 imes 8x = -73.6x[/tex]
      [tex]-9.2 imes (-4) = 36.8[/tex]

    • Multiply [tex]0.7[/tex] by each term inside the second parentheses:
      [tex]0.7 imes 2 = 1.4[/tex]
      [tex]0.7 imes 6.3x = 4.41x[/tex]

  2. Combine the results:

    After distributing, your expression will be:
    [tex]-73.6x + 36.8 + 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]

  4. Write the simplified expression:

    The expression simplifies to:
    [tex]-69.19x + 38.2[/tex]

Thus, the answer is option B, [tex]-69.19x + 38.2[/tex].

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