Question

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question

solve: \\((11u)(3u - 5) = 0\\). multiple answers, if any, should be separated by commas. enter your answer as an integer or a fraction(s).

provide your answer below:

\\(u = \\)

Explanation:

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<reasoning>

Identify the given equation

We are given a factored quadratic equation to solve for \(u\):
\[(11u)(3u - 5) = 0\]

Apply the Zero Product Property

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero:
\[11u = 0 \quad \text{or} \quad 3u - 5 = 0\]

Solve the first linear equation

Solve for \(u\) in the first equation by dividing both sides by \(11\):
\[u = \frac{0}{11}\]
\[u = 0\]

Solve the second linear equation

Solve for \(u\) in the second equation by first adding \(5\) to both sides:
\[3u = 5\]
Now, divide both sides by \(3\) to isolate \(u\):
\[u = \frac{5}{3}\]

Combine the solutions

The solutions to the equation are:
\[u = 0, \frac{5}{3}\]
</reasoning>

<answer>
Solve: \((11u)(3u - 5) = 0\). Multiple answers, if any, should be separated by a comma. Enter fractional answers as simplified fraction(s).

Provide your answer below:

\(u =\) <blank>\(0, \frac{5}{3}\)</blank>
</answer>

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Answer:

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</pre_analysis>

<reasoning>

Identify the given equation

We are given a factored quadratic equation to solve for \(u\):
\[(11u)(3u - 5) = 0\]

Apply the Zero Product Property

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero:
\[11u = 0 \quad \text{or} \quad 3u - 5 = 0\]

Solve the first linear equation

Solve for \(u\) in the first equation by dividing both sides by \(11\):
\[u = \frac{0}{11}\]
\[u = 0\]

Solve the second linear equation

Solve for \(u\) in the second equation by first adding \(5\) to both sides:
\[3u = 5\]
Now, divide both sides by \(3\) to isolate \(u\):
\[u = \frac{5}{3}\]

Combine the solutions

The solutions to the equation are:
\[u = 0, \frac{5}{3}\]
</reasoning>

<answer>
Solve: \((11u)(3u - 5) = 0\). Multiple answers, if any, should be separated by a comma. Enter fractional answers as simplified fraction(s).

Provide your answer below:

\(u =\) <blank>\(0, \frac{5}{3}\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Zero Product Property"
]
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