In the equation 2(x + 1) = 12, after applying the first operation, what is the resultant equation?
Understand the Problem
The question is asking us to perform the first operation on the equation 2(x + 1) = 12, which involves simplifying or manipulating the equation. This will help us determine what the new equation looks like after the first step.
Answer
The new equation is $2x + 2 = 12$.
Answer for screen readers
The new equation after the first operation is:
$$ 2x + 2 = 12 $$
Steps to Solve
- Distribute the 2 We start by distributing the 2 across the parentheses in the equation. This means we multiply 2 by both terms inside the brackets.
$$ 2(x + 1) = 2 \cdot x + 2 \cdot 1 $$
This simplifies to:
$$ 2x + 2 = 12 $$
- Set the new equation After distribution, we rewrite the equation with the new simplified form.
The equation now is:
$$ 2x + 2 = 12 $$
- Ready for next step After this operation, we can proceed to solve for $x$ in the next steps if required.
The new equation after the first operation is:
$$ 2x + 2 = 12 $$
More Information
This step is crucial as it sets the foundation for further simplification and solving the equation for the unknown variable $x$.
Tips
- Forgetting to distribute correctly when multiplying with parentheses.
- Mixing up signs, especially with negative numbers if they were present.
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