simplify the expression.
1. $7x + 15x$
2. $8y - 14y$
3. $7d + 9 - 5d$
4. $3w + 2(2 - 3w) + 2$
5. $(x + 3) + (3x - 7)$
6. $(5k + 6) + (4k - 8)$
7. $(-7n + 6) + (5n + 15)$
8. $(9z + 12) - (6z + 8)$
9. $(8b + 1) - (-10b - 5)$
10. $s(8 - 2t) + 3t(4 - 2s) + 5t$
11. $qr + 2q^2 - 3qr - r^2 - 6q^2$
12. $g^3(h - 4g) - h(3 - 2g^3)$
13. earnings the original price of a model car is $d$ dollars. you use a coupon and buy the kit for $(d - 10)$ dollars. you assemble the model car and sell it for $(2d - 20)$ dollars. write an expression that represents your earnings. interpret the expression.

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{ "quality": "clear", "question_count": 13, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Algebraic Simplification", "Order of Operations" ], "new_concepts": [ "Polynomial Operations", "Algebraic Modeling" ], "current_concepts": [ "Distributive Property", "Algebraic Simplification", "Order of Operations", "Polynomial Operations", "Algebraic Modeling" ] } ## Simplify expressions 1 through 3 $$ \begin{aligned} &\text{1. } 7x + 15x = (7 + 15)x = 22x\ &\text{2. } 8y - 14y = (8 - 14)y = -6y\ &\text{3. } 7d + 9 - 5d = (7d - 5d) + 9 = 2d + 9 \end{aligned} $$ ## Simplify expressions 4 through 8 $$ \begin{aligned} &\text{4. } 3w + 2(2 - 3w) + 2 = 3w + 4 - 6w + 2 = -3w + 6\ &\text{5. } (x + 3) + (3x - 7) = x + 3 + 3x - 7 = 4x - 4\ &\text{6. } (5k + 6) + (4k - 8) = 5k + 6 + 4k - 8 = 9k - 2\ &\text{7. } (-7n + 6) + (5n + 15) = -7n + 6 + 5n + 15 = -2n + 21\ &\text{8. } (9z + 12) - (6z + 8) = 9z + 12 - 6z - 8 = 3z + 4 \end{aligned} $$ ## Simplify expressions 9 through 13 $$ \begin{aligned} &\text{9. } (8b + 1) - (-10b - 5) = 8b + 1 + 10b + 5 = 18b + 6\ &\text{10. } s(8 - 2t) + 3t(4 - 2s) + 5t = 8s - 2st + 12t - 6st + 5t = 8s - 8st + 17t\ &\text{11. } qr + 2q^2 - 3qr - r^2 - 6q^2 = -2qr - 4q^2 - r^2\ &\text{12. } g^3(h - 4g) - h(3 - 2g^3) = g^3h - 4g^4 - 3h + 2g^3h = 3g^3h - 4g^4 - 3h\ &\text{13. } \text{Earnings} = \text{Selling Price} - \text{Purchase Price} = (2d - 20) - (d - 10) = 2d - 20 - d + 10 = d - 10 \end{aligned} $$ | No. | Answer | |---|---| | 1 | $22x$ | | 2 | $-6y$ | | 3 | $2d + 9$ | | 4 | $-3w + 6$ | | 5 | $4x - 4$ | | 6 | $9k - 2$ | | 7 | $-2n + 21$ | | 8 | $3z + 4$ | | 9 | $18b + 6$ | | 10 | $8s - 8st + 17t$ | | 11 | $-4q^2 - 2qr - r^2$ | | 12 | $-4g^4 + 3g^3h - 3h$ | | 13 | Expression: $d - 10$. Interpretation: Your earnings are $10$ dollars less than the original price of the model car. | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Simplification" ] }

No.	Answer
2	\(-6y\)
3	\(2d + 9\)
4	\(-3w + 6\)
5	\(4x - 4\)
6	\(9k - 2\)
7	\(-2n + 21\)
8	\(3z + 4\)
9	\(18b + 6\)
10	\(8s - 8st + 17t\)
11	\(-4q^2 - 2qr - r^2\)
12	\(-4g^4 + 3g^3h - 3h\)
13	Expression: \(d - 10\). Interpretation: Your earnings are \(10\) dollars less than the original price of the model car.

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Explanation:

Simplify expressions 1 through 3

Simplify expressions 4 through 8

Simplify expressions 9 through 13

Answer: