Alanna tried to solve an equation:
[tex]\begin{array}{rlr}
4 c & =12 & \\
\frac{4 c}{4} & =12 \cdot 4 & \text { Setting up } \\
c & =48 & \text { Calculating }
\end{array}[/tex]
Where did Alanna make her first mistake?
Choose 1 answer:
A. Setting up
B. Calculating
C. Alanna correctly solved the equation.
Answer (2)
Start with the equation 4 c = 12 .
To isolate c , divide both sides by 4: 4 4 c = 4 12 .
Simplify to find c = 3 .
Alanna incorrectly multiplied 12 by 4 instead of dividing, so the mistake was in the 'Setting up' step. The answer is (A).
Explanation
Analyze the problem The problem is to identify where Alanna made a mistake while solving the equation 4 c = 12 . Let's analyze the steps.
Isolate the variable The initial equation is 4 c = 12 . To isolate c , we need to divide both sides of the equation by 4.
Correct step The correct step should be: 4 4 c = 4 12
Simplify the equation This simplifies to: c = 3
Identify the mistake Alanna's step was: 4 4 c = 12 ⋅ 4 This shows that Alanna multiplied the right side by 4 instead of dividing by 4. This is where the mistake occurred.
Conclusion Therefore, Alanna made her first mistake in the 'Setting up' step by multiplying 12 by 4 instead of dividing by 4.
Examples
In real life, solving equations like this is crucial for various tasks, such as determining the cost of individual items when you know the total cost of a set. For example, if 4 identical items cost $12, this equation helps you find the cost of one item, which is $3. Understanding how to correctly isolate variables in equations is a fundamental skill in algebra and has numerous practical applications.
Alanna made her first mistake in the 'Setting up' step by multiplying 12 by 4 instead of dividing it by 4. The correct solution is that c should equal 3 after properly dividing both sides of the equation by 4. Therefore, the answer is (A).
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