Question

solve for (x) and graph the solution on the number line below.

80 < 10x

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": true,
"concepts_used": [],
"new_concepts": [
"Linear Inequalities",
"Number Line Graphing"
],
"current_concepts": [
"Linear Inequalities",
"Number Line Graphing"
]
}
</pre_analysis>

<reasoning>

Dividir ambos lados entre 10

\[

$$\begin{aligned} 80 &< 10x \\ \frac{80}{10} &< x \\ 8 &< x \end{aligned}$$

\]

Reescribir la desigualdad

\[
x > 8
\]
</reasoning>

<answer>
Solve for \(x\) and graph the solution on the number line below.

\(80 < 10x\)

Inequality Notation: <blank>\(x > 8\)</blank>
</answer>

<plot>
{
"elements": [
{
"type": "line",
"params": [[-14, 0], [14, 0]],
"properties": {
"strokeColor": "#583C87",
"strokeWidth": 2,
"fixed": true
}
},
{
"type": "bentinequality",
"params": [{ "x": 8, "operator": ">", "labelText": "x > 8" }],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3
}
},
{
"type": "point",
"params": [[8, 0]],
"properties": {
"name": "8",
"size": 4,
"fillColor": "white",
"strokeColor": "#8C55F2",
"strokeWidth": 2,
"withLabel": true
}
}
],
"timestamps": [0.1]
}
</plot>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": true,
"concepts_used": [],
"new_concepts": [
"Linear Inequalities",
"Number Line Graphing"
],
"current_concepts": [
"Linear Inequalities",
"Number Line Graphing"
]
}
</pre_analysis>

<reasoning>

Dividir ambos lados entre 10

\[

$$\begin{aligned} 80 &< 10x \\ \frac{80}{10} &< x \\ 8 &< x \end{aligned}$$

\]

Reescribir la desigualdad

\[
x > 8
\]
</reasoning>

<answer>
Solve for \(x\) and graph the solution on the number line below.

\(80 < 10x\)

Inequality Notation: <blank>\(x > 8\)</blank>
</answer>

<plot>
{
"elements": [
{
"type": "line",
"params": [[-14, 0], [14, 0]],
"properties": {
"strokeColor": "#583C87",
"strokeWidth": 2,
"fixed": true
}
},
{
"type": "bentinequality",
"params": [{ "x": 8, "operator": ">", "labelText": "x > 8" }],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3
}
},
{
"type": "point",
"params": [[8, 0]],
"properties": {
"name": "8",
"size": 4,
"fillColor": "white",
"strokeColor": "#8C55F2",
"strokeWidth": 2,
"withLabel": true
}
}
],
"timestamps": [0.1]
}
</plot>

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