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Answer :
Sure, let's simplify the expression step by step:
The expression we need to simplify is:
[tex]\[ -9.2(8x - 4) + 0.7(2 + 6.3x) \][/tex]
Step 1: Distribute the factors inside each set of parentheses.
1. For 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]
So this part becomes:
[tex]\[ -73.6x + 36.8 \][/tex]
2. For 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]
So this part becomes:
[tex]\[ 1.4 + 4.41x \][/tex]
Step 2: Combine like terms.
- Combine the terms with [tex]\(x\)[/tex]:
[tex]\[ -73.6x + 4.41x = -69.19x \][/tex]
- Combine the constant terms:
[tex]\[ 36.8 + 1.4 = 38.2 \][/tex]
Therefore, the simplified expression is:
[tex]\[ -69.19x + 38.2 \][/tex]
This corresponds to the choice:
[tex]\[ -69.19x + 38.2 \][/tex]
The expression we need to simplify is:
[tex]\[ -9.2(8x - 4) + 0.7(2 + 6.3x) \][/tex]
Step 1: Distribute the factors inside each set of parentheses.
1. For 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]
So this part becomes:
[tex]\[ -73.6x + 36.8 \][/tex]
2. For 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]
So this part becomes:
[tex]\[ 1.4 + 4.41x \][/tex]
Step 2: Combine like terms.
- Combine the terms with [tex]\(x\)[/tex]:
[tex]\[ -73.6x + 4.41x = -69.19x \][/tex]
- Combine the constant terms:
[tex]\[ 36.8 + 1.4 = 38.2 \][/tex]
Therefore, the simplified expression is:
[tex]\[ -69.19x + 38.2 \][/tex]
This corresponds to the choice:
[tex]\[ -69.19x + 38.2 \][/tex]
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