Which expression is equivalent to the algebraic expression 3.5(3x + 2)?

Understand the Problem

The question is asking which expression is equivalent to the algebraic expression 3.5(3x + 2). We need to simplify or expand this expression to identify the equivalent form from the given options.

Answer

$10.5x + 7$

Steps to Solve

Distribute the 3.5 Multiply 3.5 by each term inside the parentheses $(3x + 2)$:

$$ 3.5(3x) + 3.5(2) $$

Calculate the products Now, calculate each product:

For the first term: $$ 3.5 \cdot 3x = 10.5x $$
For the second term: $$ 3.5 \cdot 2 = 7 $$

Combine the results Combine the simplified terms to express the final result:

$$ 10.5x + 7 $$

The equivalent expression is $10.5x + 7$.

More Information

This process involved distributing a scalar across a binomial expression. The result can help simplify algebraic equations or expressions often found in various mathematical problems.

Tips

Failing to distribute correctly: Ensure that both terms inside the parentheses are multiplied by the number outside.
Forgetting to simplify after distribution: Always combine like terms when possible.

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