name:
solving inequalities
solve and graph the given inequalities on a number line.

\$4(2x - 3) \ge -8\$

\$4x + 6 \le 18\$

\$-10 < 6x + 2\$

\$4(x - 2) > 20\$

\$6x + 7 < 37\$

\$6 - 5x > -10\$

\$7 + 4x \ge 19\$

\$5y < 8 - 7\$

\$6x - 7 \le 5\$

\$6x + 2 \le 32\$

Question

name:
solving inequalities
solve and graph the given inequalities on a number line.

\$4(2x - 3) \ge -8\$
\$4x + 6 \le 18\$
\$-10 < 6x + 2\$
\$4(x - 2) > 20\$
\$6x + 7 < 37\$
\$6 - 5x > -10\$
\$7 + 4x \ge 19\$
\$5y < 8 - 7\$
\$6x - 7 \le 5\$
\$6x + 2 \le 32\$

Accepted Answer

{ "quality": "clear", "question_count": 10, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Inequalities" ], "new_concepts": [], "current_concepts": [ "Solving Inequalities", "Number Line Representation" ] } ## Solve Question 1 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 4(2x - 3) &\ge -8 \ 2x - 3 &\ge -2 \ 2x &\ge 1 \ x &\ge \frac{1}{2} \end{aligned} $$ ## Solve Question 2 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 4x + 6 &\le 18 \ 4x &\le 12 \ x &\le 3 \end{aligned} $$ ## Solve Question 3 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} -10 &< 6x + 2 \ -12 &< 6x \ -2 &< x \ x &> -2 \end{aligned} $$ ## Solve Question 4 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 4(x - 2) &> 20 \ x - 2 &> 5 \ x &> 7 \end{aligned} $$ ## Solve Question 5 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 6x + 7 &< 37 \ 6x &< 30 \ x &< 5 \end{aligned} $$ ## Solve Question 6 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 6 - 5x &> -10 \ -5x &> -16 \ x &< \frac{16}{5} \quad (3.2) \end{aligned} $$ ## Solve Question 7 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 7 + 4x &\ge 19 \ 4x &\ge 12 \ x &\ge 3 \end{aligned} $$ ## Solve Question 8 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 5y &< 8 - 7 \ 5y &< 1 \ y &< \frac{1}{5} \quad (0.2) \end{aligned} $$ ## Solve Question 9 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 6x - 7 &\le 5 \ 6x &\le 12 \ x &\le 2 \end{aligned} $$ ## Solve Question 10 Using the *Solving Inequalities* knowledge point $$ \begin{aligned} 6x + 2 &\le 32 \ 6x &\le 30 \ x &\le 5 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $4(2x - 3) \ge -8$ | $x \ge \frac{1}{2}$ | | 2 | $4x + 6 \le 18$ | $x \le 3$ | | 3 | $-10 < 6x + 2$ | $x > -2$ | | 4 | $4(x - 2) > 20$ | $x > 7$ | | 5 | $6x + 7 < 37$ | $x < 5$ | | 6 | $6 - 5x > -10$ | $x < \frac{16}{5}$ | | 7 | $7 + 4x \ge 19$ | $x \ge 3$ | | 8 | $5y < 8 - 7$ | $y < \frac{1}{5}$ | | 9 | $6x - 7 \le 5$ | $x \le 2$ | | 10 | $6x + 2 \le 32$ | $x \le 5$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Inequalities" ] }

No.	Problem	Answer
2	\(4x + 6 \le 18\)	\(x \le 3\)
3	\(-10 < 6x + 2\)	\(x > -2\)
4	\(4(x - 2) > 20\)	\(x > 7\)
5	\(6x + 7 < 37\)	\(x < 5\)
6	\(6 - 5x > -10\)	\(x < \frac{16}{5}\)
7	\(7 + 4x \ge 19\)	\(x \ge 3\)
8	\(5y < 8 - 7\)	\(y < \frac{1}{5}\)
9	\(6x - 7 \le 5\)	\(x \le 2\)
10	\(6x + 2 \le 32\)	\(x \le 5\)

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