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Answer :
Sure! Let's simplify the expression [tex]\(-9.2(8x - 4) + 0.7(2 + 6.3x)\)[/tex] step by step.
1. Distribute the [tex]\(-9.2\)[/tex] across the terms inside the first parenthesis:
[tex]\[
-9.2(8x - 4) = -9.2 \times 8x + (-9.2) \times (-4)
\][/tex]
[tex]\[
= -73.6x + 36.8
\][/tex]
2. Distribute the [tex]\(0.7\)[/tex] across the terms inside the second parenthesis:
[tex]\[
0.7(2 + 6.3x) = 0.7 \times 2 + 0.7 \times 6.3x
\][/tex]
[tex]\[
= 1.4 + 4.41x
\][/tex]
3. Combine all the distributed parts:
[tex]\[
(-73.6x + 36.8) + (1.4 + 4.41x)
\][/tex]
4. 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]
5. Write the simplified expression:
[tex]\[
-69.19x + 38.2
\][/tex]
Therefore, the simplified form of the expression is [tex]\(-69.19x + 38.2\)[/tex], which corresponds to the option:
[tex]\[
-69.19x + 38.2
\][/tex]
1. Distribute the [tex]\(-9.2\)[/tex] across the terms inside the first parenthesis:
[tex]\[
-9.2(8x - 4) = -9.2 \times 8x + (-9.2) \times (-4)
\][/tex]
[tex]\[
= -73.6x + 36.8
\][/tex]
2. Distribute the [tex]\(0.7\)[/tex] across the terms inside the second parenthesis:
[tex]\[
0.7(2 + 6.3x) = 0.7 \times 2 + 0.7 \times 6.3x
\][/tex]
[tex]\[
= 1.4 + 4.41x
\][/tex]
3. Combine all the distributed parts:
[tex]\[
(-73.6x + 36.8) + (1.4 + 4.41x)
\][/tex]
4. 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]
5. Write the simplified expression:
[tex]\[
-69.19x + 38.2
\][/tex]
Therefore, the simplified form of the expression is [tex]\(-69.19x + 38.2\)[/tex], which corresponds to the option:
[tex]\[
-69.19x + 38.2
\][/tex]
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