which of the $x$ values are solutions to the inequality $4(2 - x) -2x - 3(4x + 1)$? choose two correct answers.

$x = 0$
$x = -2.2$
$x = -1.1$
$x = -10$
$x = 10$

Question

which of the $x$ values are solutions to the inequality $4(2 - x) > -2x - 3(4x + 1)$? choose two correct answers.

$x = 0$
$x = -2.2$
$x = -1.1$
$x = -10$
$x = 10$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Solving Linear Inequalities", "Distributive Property", "Inequality Properties" ], "new_concepts": [], "current_concepts": [ "Solving Linear Inequalities", "Distributive Property", "Inequality Properties" ] } ## Expand both sides of the inequality Using the **Distributive Property** knowledge point $$ \begin{aligned} 4(2 - x) &> -2x - 3(4x + 1) \ 8 - 4x &> -2x - 12x - 3 \end{aligned} $$ ## Simplify the right side Using the **Solving Linear Inequalities** knowledge point $$ \begin{aligned} 8 - 4x &> -14x - 3 \end{aligned} $$ ## Isolate the variable terms Using the **Inequality Properties** knowledge point $$ \begin{aligned} 8 - 4x + 14x &> -3 \ 8 + 10x &> -3 \ 10x &> -11 \end{aligned} $$ ## Solve for x Using the **Solving Linear Inequalities** knowledge point $$ \begin{aligned} x &> -\frac{11}{10} \ x &> -1.1 \end{aligned} $$ ## Identify the correct values Using the **Solving Linear Inequalities** knowledge point $$ \begin{aligned} &\text{We need values strictly greater than } -1.1:\ &x = 0 \implies 0 > -1.1 \quad (\text{True})\ &x = -2.2 \implies -2.2 > -1.1 \quad (\text{False})\ &x = -1.1 \implies -1.1 > -1.1 \quad (\text{False})\ &x = -10 \implies -10 > -1.1 \quad (\text{False})\ &x = 10 \implies 10 > -1.1 \quad (\text{True}) \end{aligned} $$

$x = 0$

$x = -2.2$

$x = -1.1$

$x = -10$

$x = 10$

{ "elements": [ { "type": "bentinequality", "params": [{ "x": -1.1, "operator": ">", "labelText": "x > -1.1" }], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "x = 0 (Solution)", "color": "#5583F2", "size": 4, "withLabel": true } }, { "type": "point", "params": [[10, 0]], "properties": { "name": "x = 10 (Solution)", "color": "#5583F2", "size": 4, "withLabel": true } }, { "type": "point", "params": [[-1.1, 0]], "properties": { "name": "-1.1 (Boundary)", "color": "#F2557F", "size": 4, "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Linear Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Expand both sides of the inequality

Simplify the right side

Isolate the variable terms

Solve for x

Identify the correct values

Answer: