10. $-4x + 7.2 = 32$
11. $7x - 3 = -9$
12. $8.4 - 2x

Question

10. $-4x + 7.2 = 32$
11. $7x - 3 = -9$
12. $8.4 - 2x < 16$
13. $7.5 - x = 26.8$
14. $-3x + 18 = -27$
15. $15x - 6 \ge -21$
16. $-4x + 8 = 40$
17. $\frac{x}{7} - 2 = 8$
18. $\frac{x}{6} + 9 \le 10$

Accepted Answer

{ "quality": "clear", "question_count": 9, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Multi-Step Equations", "Solving Linear Inequalities" ], "new_concepts": [], "current_concepts": [ "Solving Multi-Step Equations", "Solving Linear Inequalities" ] } ## Solve Question 10 Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} -4x + 7.2 &= 32 \ -4x &= 32 - 7.2 \ -4x &= 24.8 \ x &= \frac{24.8}{-4} \ x &= -6.2 \end{aligned} $$ ## Solve Question 11 Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} 7x - 3 &= -9 \ 7x &= -9 + 3 \ 7x &= -6 \ x &= -\frac{6}{7} \end{aligned} $$ ## Solve Question 12 Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} 8.4 - 2x &< 16 \ -2x &< 16 - 8.4 \ -2x &< 7.6 \ x &> \frac{7.6}{-2} \ x &> -3.8 \end{aligned} $$ ## Solve Question 13 Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} 7.5 - x &= 26.8 \ -x &= 26.8 - 7.5 \ -x &= 19.3 \ x &= -19.3 \end{aligned} $$ ## Solve Question 14 Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} -3x + 18 &= -27 \ -3x &= -27 - 18 \ -3x &= -45 \ x &= \frac{-45}{-3} \ x &= 15 \end{aligned} $$ ## Solve Question 15 Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} 15x - 6 &\ge -21 \ 15x &\ge -21 + 6 \ 15x &\ge -15 \ x &\ge \frac{-15}{15} \ x &\ge -1 \end{aligned} $$ ## Solve Question 16 Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} -4x + 8 &= 40 \ -4x &= 40 - 8 \ -4x &= 32 \ x &= \frac{32}{-4} \ x &= -8 \end{aligned} $$ ## Solve Question 17 Using the *Solving Multi-Step Equations* knowledge point $$ \begin{aligned} \frac{x}{7} - 2 &= 8 \ \frac{x}{7} &= 8 + 2 \ \frac{x}{7} &= 10 \ x &= 10 \cdot 7 \ x &= 70 \end{aligned} $$ ## Solve Question 18 Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} \frac{x}{6} + 9 &\le 10 \ \frac{x}{6} &\le 10 - 9 \ \frac{x}{6} &\le 1 \ x &\le 1 \cdot 6 \ x &\le 6 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 10 | $-4x + 7.2 = 32$ | $x = -6.2$ | | 11 | $7x - 3 = -9$ | $x = -\frac{6}{7}$ | | 12 | $8.4 - 2x < 16$ | $x > -3.8$ | | 13 | $7.5 - x = 26.8$ | $x = -19.3$ | | 14 | $-3x + 18 = -27$ | $x = 15$ | | 15 | $15x - 6 \ge -21$ | $x \ge -1$ | | 16 | $-4x + 8 = 40$ | $x = -8$ | | 17 | $\frac{x}{7} - 2 = 8$ | $x = 70$ | | 18 | $\frac{x}{6} + 9 \le 10$ | $x \le 6$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Multi-Step Equations" ] }

No.	Problem	Answer
11	\(7x - 3 = -9\)	\(x = -\frac{6}{7}\)
12	\(8.4 - 2x < 16\)	\(x > -3.8\)
13	\(7.5 - x = 26.8\)	\(x = -19.3\)
14	\(-3x + 18 = -27\)	\(x = 15\)
15	\(15x - 6 \ge -21\)	\(x \ge -1\)
16	\(-4x + 8 = 40\)	\(x = -8\)
17	\(\frac{x}{7} - 2 = 8\)	\(x = 70\)
18	\(\frac{x}{6} + 9 \le 10\)	\(x \le 6\)

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