15 linear equation practice questions
solve x
1. $\frac{3}{4}(2x + 5) = 12$
2. $\frac{2}{3}(5x - 1) = 8$
3. $4(x + 3) = 7 - 5(x - 2)$
4. $3 - 4(3x + 2) = 2(5 - x)$
5. $6(x - 3) = 5x$
6. $\frac{1}{3}(4x + 2) = 2$
7. $\frac{1}{3}x + 2 = \frac{1}{4}x - 1$
8. $\frac{3}{5}x - 4 = \frac{2}{5}x + 3$
9. $\frac{x + 2}{8} - 2 = \frac{3x - 6}{4}$
10. $\frac{2x - 5}{6} + 1 = \frac{4x + 3}{2}$

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{ "quality": "clear", "question_count": 10, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Linear Equations", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Solving Linear Equations", "Distributive Property" ] } ## Solve equations 1 to 4 $$ \begin{aligned} 1. \quad &\frac{3}{4}(2x + 5) = 12 \implies 2x + 5 = 16 \implies 2x = 11 \implies x = \frac{11}{2}\ 2. \quad &\frac{2}{3}(5x - 1) = 8 \implies 5x - 1 = 12 \implies 5x = 13 \implies x = \frac{13}{5}\ 3. \quad &4(x + 3) = 7 - 5(x - 2) \implies 4x + 12 = 7 - 5x + 10 \implies 9x = 5 \implies x = \frac{5}{9}\ 4. \quad &3 - 4(3x + 2) = 2(5 - x) \implies 3 - 12x - 8 = 10 - 2x \implies -10x = 15 \implies x = -\frac{3}{2} \end{aligned} $$ ## Solve equations 5 to 7 $$ \begin{aligned} 5. \quad &6(x - 3) = 5x \implies 6x - 18 = 5x \implies x = 18\ 6. \quad &\frac{1}{3}(4x + 2) = 2 \implies 4x + 2 = 6 \implies 4x = 4 \implies x = 1\ 7. \quad &\frac{1}{3}x + 2 = \frac{1}{4}x - 1 \implies \frac{1}{12}x = -3 \implies x = -36 \end{aligned} $$ ## Solve equations 8 to 10 $$ \begin{aligned} 8. \quad &\frac{3}{5}x - 4 = \frac{2}{5}x + 3 \implies \frac{1}{5}x = 7 \implies x = 35\ 9. \quad &\frac{x + 2}{8} - 2 = \frac{3x - 6}{4} \implies x + 2 - 16 = 2(3x - 6) \implies x - 14 = 6x - 12 \implies -5x = 2 \implies x = -\frac{2}{5}\ 10. \quad &\frac{2x - 5}{6} + 1 = \frac{4x + 3}{2} \implies 2x - 5 + 6 = 3(4x + 3) \implies 2x + 1 = 12x + 9 \implies -10x = 8 \implies x = -\frac{4}{5} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $\frac{3}{4}(2x + 5) = 12$ | $x = \frac{11}{2}$ | | 2 | $\frac{2}{3}(5x - 1) = 8$ | $x = \frac{13}{5}$ | | 3 | $4(x + 3) = 7 - 5(x - 2)$ | $x = \frac{5}{9}$ | | 4 | $3 - 4(3x + 2) = 2(5 - x)$ | $x = -\frac{3}{2}$ | | 5 | $6(x - 3) = 5x$ | $x = 18$ | | 6 | $\frac{1}{3}(4x + 2) = 2$ | $x = 1$ | | 7 | $\frac{1}{3}x + 2 = \frac{1}{4}x - 1$ | $x = -36$ | | 8 | $\frac{3}{5}x - 4 = \frac{2}{5}x + 3$ | $x = 35$ | | 9 | $\frac{x + 2}{8} - 2 = \frac{3x - 6}{4}$ | $x = -\frac{2}{5}$ | | 10 | $\frac{2x - 5}{6} + 1 = \frac{4x + 3}{2}$ | $x = -\frac{4}{5}$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Linear Equations" ] }

No.	Problem	Answer
2	\(\frac{2}{3}(5x - 1) = 8\)	\(x = \frac{13}{5}\)
3	\(4(x + 3) = 7 - 5(x - 2)\)	\(x = \frac{5}{9}\)
4	\(3 - 4(3x + 2) = 2(5 - x)\)	\(x = -\frac{3}{2}\)
5	\(6(x - 3) = 5x\)	\(x = 18\)
6	\(\frac{1}{3}(4x + 2) = 2\)	\(x = 1\)
7	\(\frac{1}{3}x + 2 = \frac{1}{4}x - 1\)	\(x = -36\)
8	\(\frac{3}{5}x - 4 = \frac{2}{5}x + 3\)	\(x = 35\)
9	\(\frac{x + 2}{8} - 2 = \frac{3x - 6}{4}\)	\(x = -\frac{2}{5}\)
10	\(\frac{2x - 5}{6} + 1 = \frac{4x + 3}{2}\)	\(x = -\frac{4}{5}\)

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