Where did Trent make his first mistake?
Understand the Problem
The question asks to identify where Trent made a mistake when solving for 'g' in the equation g/3 = 4/3. The steps shown include multiplying both sides by 3, but the right side of the equation is incorrectly multiplied by 1/3 instead of 3.
Answer
Trent's mistake was multiplying the right side by $\frac{1}{3}$ instead of 3.
Answer for screen readers
Trent made his first mistake when he multiplied the right side of the equation by $\frac{1}{3}$ instead of 3.
Steps to Solve
- Identify the goal
The goal is to isolate $g$ to find its value.
- Analyze the first step
The original equation is $\frac{g}{3} = \frac{4}{3}$. To isolate $g$, we need to multiply both sides of the equation by 3.
- Analyze Trent's setup
Trent wrote $\frac{g}{3} \cdot 3 = \frac{4}{3} \cdot \frac{1}{3}$. He correctly multiplied the left side by 3. However, he incorrectly multiplied the right side by $\frac{1}{3}$ instead of 3. That's where his mistake is.
- Correct the right side
The correct setup should be $\frac{g}{3} \cdot 3 = \frac{4}{3} \cdot 3$.
- Solve the equation correctly
$\frac{g}{3} \cdot 3 = \frac{4}{3} \cdot 3$ simplifies to $g = \frac{12}{3}$, and further simplifies to $g = 4$.
Trent made his first mistake when he multiplied the right side of the equation by $\frac{1}{3}$ instead of 3.
More Information
To solve for a variable, we must perform the same operation on both sides of the equation to maintain equality.
Tips
A common mistake is not performing the same operation on both sides of the equation, as seen in Trent's incorrect multiplication of the right side by $\frac{1}{3}$ instead of 3.
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