Question

1. select all expressions that are equivalent to ((7x + 6)+(4x + 7)) a (7x + 12) b (11x + 12) c (5 + 11x + 7) d (7x + 12 + 4x) 10. simplify the expression (7x - 4x + 3 - 2x - 1) 11. simplify the expression (4x + 3x + 8 - 3x - 3) 12. select all expressions that are equivalent to (8x + 24) a (8(x - 2)) b (8(x + 3)) c (8(x + 24)) d (4(2x + 6)) 12. select all expressions that are equivalent to (10x + (2x - 5)+ 4x) a (12x - 5) b (12x - 5 + 4x) c (14x - 5 + 4x) d (16x - 5) 9. select all expressions that are equivalent to (5x - 2x + 7 + 2x + 5) a (3x + 12) b (7 + 5x + 5) c (5x + 12) d (5 + 12x) 13. select all expressions that are equivalent to (9x - 36) a (12(x - 36)) b (6(2x - 6)) c (9(x - 4)) d (3(3x - 12)) 14. simplify the expression (5x - (3x + 2)+ 2x) 15. simplify the expression (6x - 2(2x + 5)+ 5x)

Explanation:

Step1: Simplify question 8

Combine like terms:
$$(7x + 5) + (4x + 7) = 7x + 4x + 5 + 7 = 11x + 12$$

Step2: Simplify question 9

Combine like terms:
$$5x - 2x + 7 + 2x + 5 = 5x + 12$$

Step3: Simplify question 10

Combine like terms:
$$7x - 4x - 2x + 3 - 1 = x + 2$$

Step4: Simplify question 11

Combine like terms:
$$4x + 3x - 3x + 9 - 3 = 4x + 6$$

Step5: Match question 12 to $8x+24$

Factor or expand each option:

• A: $8(x-2)=8x-16$
• B: $8(x+3)=8x+24$
• C: $8(x+24)=8x+192$
• D: $4(2x+6)=8x+24$

Step6: Simplify question 12 (original expression)

Expand and combine like terms:
$$10x + (2x - 5) + 4x = 10x + 2x + 4x - 5 = 16x - 5$$

Step7: Simplify question 14

Expand and combine like terms:
$$5x - (3x + 2) + 2x = 5x - 3x + 2x - 2 = 4x - 2$$

Step8: Simplify question 15

Expand and combine like terms:
$$6x - 2(2x + 5) + 5x = 6x - 4x + 5x - 10 = 7x - 10$$

Answer:

1. B. $11x + 12$
2. C. $5x + 12$
3. $x + 2$
4. $4x + 6$
5. B. $8(x + 3)$, D. $4(2x + 6)$
6. D. $16x - 5$
7. $4x - 2$
8. $7x - 10$

Note: Question 13 is incomplete and cannot be solved with the provided content.