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Which algebraic expression is equivalent to the expression below?

[tex]\[ 3(5x + 7) - 6(4 - 2x) \][/tex]

A. [tex]\( 27x - 12 \)[/tex]
B. [tex]\( 27x - 3 \)[/tex]
C. [tex]\( 12x + 3 \)[/tex]
D. [tex]\( 12x + 27 \)[/tex]

Sagot :

GinnyAnsweridn
Let's solve the given algebraic expression step by step:

The expression is:
[tex]\[ 3(5x + 7) - 6(4 - 2x) \][/tex]

Step 1: Distribute the constants inside the parentheses.
- Distributing [tex]\(3\)[/tex] into [tex]\((5x + 7)\)[/tex]:
[tex]\[ 3 \cdot 5x + 3 \cdot 7 = 15x + 21 \][/tex]
- Distributing [tex]\(-6\)[/tex] into [tex]\((4 - 2x)\)[/tex]:
[tex]\[ -6 \cdot 4 + (-6) \cdot (-2x) = -24 + 12x \][/tex]

Step 2: Combine the expressions.
[tex]\[ 15x + 21 - 24 + 12x \][/tex]

Step 3: Combine like terms.
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 15x + 12x = 27x \][/tex]
- Combine the constant terms:
[tex]\[ 21 - 24 = -3 \][/tex]

So, the resulting expression is:
[tex]\[ 27x - 3 \][/tex]

From the provided options:
- [tex]\(27x - 12\)[/tex]
- [tex]\(27x - 3\)[/tex]
- [tex]\(12x + 3\)[/tex]
- [tex]\(12x + 27\)[/tex]

The equivalent expression to the given algebraic expression is:
[tex]\[ 27x - 3 \][/tex]

Therefore, the correct answer is:
[tex]\[ 27x - 3 \][/tex]
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