Question

10,326 Learners found this answer helpful

solve.

\\\frac{4}{3+z} = \frac{2}{3}\\

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Proportions",
"Cross Product Property",
"Solving Algebraic Equations"
],
"new_concepts": [],
"current_concepts": [
"Proportions",
"Cross Product Property",
"Solving Algebraic Equations"
]
}
</pre_analysis>

<reasoning>

Set up the proportion equation

\[
\frac{4}{3+z} = \frac{2}{3}
\]

Apply the cross product property

\[
4 \cdot 3 = 2 \cdot (3 + z)
\]
\[
12 = 6 + 2z
\]

Solve for z

\[
12 - 6 = 2z
\]
\[
6 = 2z
\]
\[
z = 3
\]
</reasoning>

<answer>
Solve.
\[\frac{4}{3+z} = \frac{2}{3}\]
\(z =\) <blank>\(3\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Algebraic Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Proportions",
"Cross Product Property",
"Solving Algebraic Equations"
],
"new_concepts": [],
"current_concepts": [
"Proportions",
"Cross Product Property",
"Solving Algebraic Equations"
]
}
</pre_analysis>

<reasoning>

Set up the proportion equation

\[
\frac{4}{3+z} = \frac{2}{3}
\]

Apply the cross product property

\[
4 \cdot 3 = 2 \cdot (3 + z)
\]
\[
12 = 6 + 2z
\]

Solve for z

\[
12 - 6 = 2z
\]
\[
6 = 2z
\]
\[
z = 3
\]
</reasoning>

<answer>
Solve.
\[\frac{4}{3+z} = \frac{2}{3}\]
\(z =\) <blank>\(3\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Algebraic Equations"
]
}
</post_analysis>