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Answer :
Let's simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] step-by-step.
1. Distribute the numbers in the expression:
Start with the first part: [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].
Now, look at the second part: [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].
2. Combine like terms:
- The terms with [tex]\(x\)[/tex] are: [tex]\(-73.6x + 4.41x\)[/tex].
[tex]\[
-73.6x + 4.41x = -69.19x.
\][/tex]
- The constant terms are: [tex]\(36.8 + 1.4\)[/tex].
[tex]\[
36.8 + 1.4 = 38.2.
\][/tex]
3. Combine everything together:
The simplified expression is:
[tex]\[
-69.19x + 38.2.
\][/tex]
So, the correct simplified expression is [tex]\(-69.19x + 38.2\)[/tex]. This matches option [tex]\( \textbf{-69.19x + 38.2} \)[/tex].
1. Distribute the numbers in the expression:
Start with the first part: [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].
Now, look at the second part: [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].
2. Combine like terms:
- The terms with [tex]\(x\)[/tex] are: [tex]\(-73.6x + 4.41x\)[/tex].
[tex]\[
-73.6x + 4.41x = -69.19x.
\][/tex]
- The constant terms are: [tex]\(36.8 + 1.4\)[/tex].
[tex]\[
36.8 + 1.4 = 38.2.
\][/tex]
3. Combine everything together:
The simplified expression is:
[tex]\[
-69.19x + 38.2.
\][/tex]
So, the correct simplified expression is [tex]\(-69.19x + 38.2\)[/tex]. This matches option [tex]\( \textbf{-69.19x + 38.2} \)[/tex].
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