Which equation could represent the first step when solving for x?
Understand the Problem
The question asks which equation represents the first step in solving the equation 7(4x + 2) + 3 = -67 for x. To solve it, we need to simplify and isolate the variable.
Answer
D: $28x + 14 + 3 = -67$
Answer for screen readers
The first step represented in the answer choices is:
$$ 28x + 14 + 3 = -67 $$
This corresponds to option D.
Steps to Solve
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Distribute the 7
We need to apply the distributive property to the left side of the equation. This means multiplying 7 by both terms inside the parentheses:
$$ 7(4x) + 7(2) + 3 = -67 $$ -
Perform the multiplication
Calculating the multiplications gives us:
$$ 28x + 14 + 3 = -67 $$ -
Combine like terms
Now we combine the constant terms (14 and 3):
$$ 28x + 17 = -67 $$ -
Identify the first step represented in the options
The correct expression that represents the first step after the distribution and combining like terms is:
$$ 28x + 14 + 3 = -67 $$
The first step represented in the answer choices is:
$$ 28x + 14 + 3 = -67 $$
This corresponds to option D.
More Information
The distributive property is a fundamental property in algebra that allows us to eliminate parentheses by distributing a multiplier to each term inside the parentheses. After distributing, combining like terms simplifies the expression, making it easier to isolate the variable.
Tips
- Not applying the distributive property correctly: Be careful to multiply the number outside the parentheses by each term inside.
- Forgetting to combine like terms: Always check your equation for any like terms that can be simplified.
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