Math  /  Algebra

QuestionApply the Distributive Property to determine the missing number.
7. 3(4+5)=34+33(4+5)=3 \cdot 4+3. \qquad 8. 5(79)=5(7)5(7-9)=5(7)- \qquad (9)
9. 4(8+y)=4(-4(8+y)=-4( \qquad ) 4y-4 y
10. 7(x6)=-7(x-6)= \qquad (x)(x)- \qquad
11. 5(37)=530+55(37)=5 \cdot 30+5. \qquad 12. 5(37)=54055(37)=5 \cdot 40-5. \qquad Which expression(s) are not equivalent to the given expression?
13. 3(x+4)3(x+4)
14. 4(3+5)-4(3+5) A. 3x+343 \cdot x+3 \cdot 4 A. 4(3)+(4)5-4(3)+(-4) 5 B. 3x+43 x+4 B. 12+(20)-12+(-20) C. 3x+123 x+12 C. 4(3)(4)5-4(3)-(-4) 5 D. 3x+73 x+7 D. -32

Jse the Distributive Property to write an equivalent expression.
15. 4(x2)4(x-2)
16. 3(a+7)3(a+7)
17. 5(b+9)-5(b+9)
18. 8(m4)-8(m-4)
19. 2(102)2(10-2)
20. 3(20+3)-3(20+3) Exercises

Studdy Solution

STEP 1

1. The Distributive Property states that a(b+c)=ab+ac a(b + c) = ab + ac .
2. We will apply the Distributive Property to each expression to find missing numbers or verify equivalency.
3. We will identify expressions that are not equivalent to the given expressions.

STEP 2

1. Apply the Distributive Property to determine missing numbers in given expressions.
2. Identify expressions that are not equivalent to the given expressions.
3. Use the Distributive Property to write equivalent expressions for given problems.

STEP 3

Apply the Distributive Property to the expression 3(4+5) 3(4+5) :
3(4+5)=34+35 3(4+5) = 3 \cdot 4 + 3 \cdot 5
Given: 3(4+5)=34+3 3(4+5) = 3 \cdot 4 + 3 .
The missing number is 35=15 3 \cdot 5 = 15 .

STEP 4

Apply the Distributive Property to the expression 5(79) 5(7-9) :
5(79)=5759 5(7-9) = 5 \cdot 7 - 5 \cdot 9
Given: 5(79)=5(7) 5(7-9) = 5(7) - .
The missing number is 59=45 5 \cdot 9 = 45 .

STEP 5

Apply the Distributive Property to the expression 4(8+y) -4(8+y) :
4(8+y)=48+(4)y -4(8+y) = -4 \cdot 8 + (-4) \cdot y
Given: 4(8+y)=4()4y -4(8+y) = -4( \quad ) - 4y .
The missing number is 48=32 -4 \cdot 8 = -32 .

STEP 6

Apply the Distributive Property to the expression 7(x6) -7(x-6) :
7(x6)=7x+76 -7(x-6) = -7 \cdot x + 7 \cdot 6
Given: 7(x6)=(x) -7(x-6) = \quad (x) - .
The missing number is 76=42 7 \cdot 6 = 42 .

STEP 7

Apply the Distributive Property to the expression 5(37) 5(37) :
5(37)=530+57 5(37) = 5 \cdot 30 + 5 \cdot 7
Given: 5(37)=530+5 5(37) = 5 \cdot 30 + 5 .
The missing number is 57=35 5 \cdot 7 = 35 .

STEP 8

Apply the Distributive Property to the expression 5(37) 5(37) again:
5(37)=54053 5(37) = 5 \cdot 40 - 5 \cdot 3
Given: 5(37)=5405 5(37) = 5 \cdot 40 - 5 .
The missing number is 53=15 5 \cdot 3 = 15 .

STEP 9

Identify expressions that are not equivalent to 3(x+4) 3(x+4) :
A. 3x+34=3x+12 3 \cdot x + 3 \cdot 4 = 3x + 12 (Equivalent) B. 3x+4 3x + 4 (Not Equivalent) C. 3x+12 3x + 12 (Equivalent) D. 3x+7 3x + 7 (Not Equivalent)
Expressions B and D are not equivalent.

STEP 10

Identify expressions that are not equivalent to 4(3+5) -4(3+5) :
A. 4(3)+(4)5=12+(20)=32 -4(3) + (-4) \cdot 5 = -12 + (-20) = -32 (Equivalent) B. 12+(20)=32 -12 + (-20) = -32 (Equivalent) C. 4(3)(4)5=12+20=8 -4(3) - (-4) \cdot 5 = -12 + 20 = 8 (Not Equivalent) D. 32-32 (Equivalent)
Expression C is not equivalent.

STEP 11

Use the Distributive Property to write equivalent expressions:
15. 4(x2)=4x8 4(x-2) = 4x - 8
16. 3(a+7)=3a+21 3(a+7) = 3a + 21
17. 5(b+9)=5b45 -5(b+9) = -5b - 45
18. 8(m4)=8m+32 -8(m-4) = -8m + 32
19. 2(102)=204=16 2(10-2) = 20 - 4 = 16
20. 3(20+3)=609=69 -3(20+3) = -60 - 9 = -69

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