write the following statements in symbols.
15. 7 more than twice a number is 11.
17. twice the sum of a number and 8 is 40.

simplify.
19. $3a + 2a$
22. $-(4y - 7)$
25. $11 - 2(x - 5)$
28. $3(x - 2) - 2(5x - 7y + 1)$

section 7-2
solve.
31. $x - 5 = 8$
34. $x - 15 = -7$
37. $x + 7 = 10$
40. $3 + y = -5$
43. $3x + 4 = 19$
46. $5 = 3x - 7$
49. $5x - 12 = 9x$
52. $4x = -28$
55. $3 = \frac{1}{5}x$

Question

write the following statements in symbols.
15. 7 more than twice a number is 11.
17. twice the sum of a number and 8 is 40.

simplify.
19. $3a + 2a$
22. $-(4y - 7)$
25. $11 - 2(x - 5)$
28. $3(x - 2) - 2(5x - 7y + 1)$

section 7-2
solve.
31. $x - 5 = 8$
34. $x - 15 = -7$
37. $x + 7 = 10$
40. $3 + y = -5$
43. $3x + 4 = 19$
46. $5 = 3x - 7$
49. $5x - 12 = 9x$
52. $4x = -28$
55. $3 = \frac{1}{5}x$

Accepted Answer

{ "quality": "clear", "question_count": 16, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Algebraic Translation", "Combining Like Terms", "Distributive Property", "Linear Equations" ], "new_concepts": [ "Multi-variable Simplification", "One-Step Equations", "Two-Step Equations" ], "current_concepts": [ "Algebraic Translation", "Combining Like Terms", "Distributive Property", "Linear Equations" ] } ## Translate statements into symbols Using the *Algebraic Translation* knowledge point $$ \begin{aligned} &\text{15. } 2x + 7 = 11\ &\text{17. } 2(x + 8) = 40 \end{aligned} $$ ## Simplify algebraic expressions Using the *Combining Like Terms* and *Distributive Property* knowledge points $$ \begin{aligned} &\text{19. } 3a + 2a = (3+2)a = 5a\ &\text{22. } -(4y - 7) = -4y + 7\ &\text{25. } 11 - 2(x - 5) = 11 - 2x + 10 = -2x + 21\ &\text{28. } 3(x - 2) - 2(5x - 7y + 1) = 3x - 6 - 10x + 14y - 2 = -7x + 14y - 8 \end{aligned} $$ ## Solve one-step linear equations Using the *Linear Equations* knowledge point $$ \begin{aligned} &\text{31. } x - 5 = 8 \implies x = 8 + 5 \implies x = 13\ &\text{34. } x - 15 = -7 \implies x = -7 + 15 \implies x = 8\ &\text{37. } x + 7 = 10 \implies x = 10 - 7 \implies x = 3\ &\text{40. } 3 + y = -5 \implies y = -5 - 3 \implies y = -8\ &\text{52. } 4x = -28 \implies x = \frac{-28}{4} \implies x = -7\ &\text{55. } 3 = \frac{1}{5}x \implies x = 3 \times 5 \implies x = 15 \end{aligned} $$ ## Solve multi-step linear equations Using the *Linear Equations* knowledge point $$ \begin{aligned} &\text{43. } 3x + 4 = 19 \implies 3x = 15 \implies x = 5\ &\text{46. } 5 = 3x - 7 \implies 12 = 3x \implies x = 4\ &\text{49. } 5x - 12 = 9x \implies -12 = 4x \implies x = -3 \end{aligned} $$ ## Write the following statements in symbols. 15. $2x + 7 = 11$ 17. $2(x + 8) = 40$ ## Simplify. 19. $5a$ 22. $-4y + 7$ 25. $-2x + 21$ 28. $-7x + 14y - 8$ ## Section 7-2: Solve. 31. $x = 13$ 34. $x = 8$ 37. $x = 3$ 40. $y = -8$ 43. $x = 5$ 46. $x = 4$ 49. $x = -3$ 52. $x = -7$ 55. $x = 15$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Translate statements into symbols

Simplify algebraic expressions

Solve one-step linear equations

Solve multi-step linear equations

Answer:

Write the following statements in symbols.

Simplify.

Section 7-2: Solve.