Add, Subtract, Factor Linear Expressions - 7th Grade Math

1. What property is shown by $(a+b)+c=a+(b+c)$?

   Associative property of addition. Grouping doesn't affect the sum when adding.

2. What is the factored form of $12x+18$ using the GCF?

   $6(2x+3)$. GCF of 12 and 18 is 6; factor it out.

3. What is the factored form of $-6x-9$ using the GCF $-3$?

   $-3(2x+3)$. Factor out -3 from both negative terms.

4. What is the simplified form of $3x+5x$?

   $8x$. Combine like terms: $3x + 5x = (3+5)x = 8x$.

5. What is the simplified form of $5x-2x+7$?

   $3x+7$. Combine like terms: $(5-2)x + 7$.

6. What is the result of expanding $3(2x-5)$?

   $6x-15$. Multiply 3 by each term: $3(2x) - 3(5)$.

7. What is the factored form of $-6x-15$ by factoring out the GCF?

   $-3(2x+5)$. Factor out GCF of $-3$: $-3(2x) + (-3)(5) = -3(2x + 5)$.

8. What property is shown by $(a+b)+c=a+(b+c)$ when regrouping terms?

   Associative property of addition. Grouping of addends doesn't change the sum.

9. What property is shown by $a(b+c)=ab+ac$?

   Distributive property. Multiplying a term by a sum equals the sum of the products.

10. What property is shown by $a(b+c)=ab+ac$ when expanding expressions?

    Distributive property. Multiplying a factor by a sum equals the sum of the products.

11. What is the simplified form of $7-3(x-2)$?

    $13-3x$. Distribute -3, then combine: $7 - 3x + 6$.

12. What property is shown by $ab=ba$ when rewriting a product in a different order?

    Commutative property of multiplication. Order of factors doesn't change the product.

13. What is the simplified form of $\frac{2}{3}x + \frac{1}{6}x$?

    $\frac{5}{6}x$. Find common denominator: $\frac{4}{6}x + \frac{1}{6}x = \frac{5}{6}x$.

14. What is the simplified form of $\frac{2}{3}x-\frac{1}{6}x$?

    $\frac{1}{2}x$. Subtract fractions: $\frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$.

15. What is the simplified form of $7y-2y$?

    $5y$. Combine like terms: $7y - 2y = (7-2)y = 5y$.

16. What property is shown by $a+b=b+a$?

    Commutative property of addition. Order doesn't matter when adding terms.

17. What is the result of expanding $\frac{3}{4}(8x+12)$?

    $6x+9$. Multiply $\frac{3}{4}$ by each term: $\frac{3 \cdot 8x}{4} + \frac{3 \cdot 12}{4}$

18. What is the expanded form of $\frac{1}{2}(6x-8)$?

    $3x-4$. Distribute $\frac{1}{2}$: $\frac{1}{2}(6x) + \frac{1}{2}(-8) = 3x - 4$.

19. What is the simplified form of $3(x-2)+2(x+5)$?

    $5x+4$. Distribute, then combine: $3x - 6 + 2x + 10 = 5x + 4$.

20. What is the result of expanding $\frac{1}{2}(6x-8)$?

    $3x-4$. Multiply $\frac{1}{2}$ by each term: $\frac{6x}{2} - \frac{8}{2}$.

21. What is the simplified form of $2(x+5)+3x$?

    $5x+10$. Expand first, then combine: $2x + 10 + 3x$.

22. What is the simplified form of $-(2x+5)+3x$?

    $x-5$. Distribute $-1$, then combine: $-2x - 5 + 3x = x - 5$.

23. What is the factored form of $9x+12$ using the GCF?

    $3(3x+4)$. Factor out GCF of 3: $3(3x) + 3(4) = 3(3x + 4)$.

24. What is the GCF factoring form for two terms $ax+ay$?

    $ax+ay=a(x+y)$. Factor out the common factor $a$ from both terms.

25. What is the rule for subtracting an expression, written as $a-(b+c)$?

    $a-(b+c)=a-b-c$. Distribute the negative sign to both terms inside parentheses.

26. What is the factored form of $14x-21$ using the GCF?

    $7(2x-3)$. Factor out GCF of 7: $7(2x) + 7(-3) = 7(2x - 3)$.

27. What is the result of expanding $-4(x+3)$?

    $-4x-12$. Multiply -4 by each term: $-4(x) + (-4)(3)$.

28. What is the simplified form of $4x+3-2x-9$?

    $2x-6$. Combine like terms: $(4-2)x + (3-9)$.

29. What is the simplified form of $\frac{1}{3}(9x+6)-2x$?

    $x+2$. Distribute $\frac{1}{3}$, then combine: $3x + 2 - 2x = x + 2$.

30. What is the expanded form of $-2(3x-5)$?

    $-6x+10$. Distribute $-2$: $-2(3x) + (-2)(-5) = -6x + 10$.

31. What is the factored form of $\frac{5}{6}x+\frac{5}{3}$ using the GCF?

    $\frac{5}{6}(x+2)$. Factor out GCF of $\frac{5}{6}$: $\frac{5}{6}(x + 2)$.

32. What is the simplified form of $4(x+3)$?

    $4x+12$. Distribute: $4 \cdot x + 4 \cdot 3 = 4x + 12$.

33. What is the simplified form of $6-2(3x-4)$?

    $-6x+14$. Distribute $-2$, then combine: $6 - 6x + 8 = -6x + 14$.

34. What is the simplified form of $\frac{3}{4}x+\frac{1}{2}x$?

    $\frac{5}{4}x$. Add fractions: $\frac{3}{4} + \frac{2}{4} = \frac{5}{4}$.

35. What is the GCF factoring form for $ax-bx$?

    $ax-bx=x(a-b)$. Factor out the common variable $x$ from both terms.

36. What is the identity for combining like terms $kx+mx$?

    $kx+mx=(k+m)x$. Combine coefficients of the same variable.

37. What is the rule for distributing a negative sign: $-(a-b)$?

    $-(a-b)=-a+b$. Negative sign changes both signs inside parentheses.

38. What is the simplified form of $2x+3-5x+1$?

    $-3x+4$. Combine like terms: $2x - 5x = -3x$ and $3 + 1 = 4$.

39. What is the factored form of $15x-10$ using the GCF?

    $5(3x-2)$. GCF of 15 and 10 is 5; factor it out.

40. What is the simplified form of $-(x-7)$?

    $-x+7$. Distribute $-1$: $-1(x) + (-1)(-7) = -x + 7$.

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