Decide upon your answer and then check the "Explanation" drop down. |
1. Explain why the following statements are equivalent: 4(x + y) = 4x + 4y
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2. Rewrite this expression using the Distributive Property: 6x + 12
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3. Using the Distributive Property, write an expression equivalent to 5(x - 6).
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4. Rewrite this expression using the Distributive Property: -5x - 25
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5. Explain why the following statements are equivalent: a + (b + 4) = a + (4 + b)
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6. Using the Commutative Property, write an equivalent expression for 5•(7x).
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7. Explain why the following equation is true: (x + 4) + (-x + (- 4)) = 0.
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8. Simplify this expression and justify your steps: 12 + 3(a + 2b) - 2a - 3b - 9 + b
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(The Explanation shown below is one possible solution.)
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12 + 3(a + 2b) - 2a - 3b - 9 + b |
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12 + 3a + 6b - 2a - 3b - 9 + b |
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12 - 9 + 3a - 2a + 6b - 3b + b |
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(12 - 9) + (3a - 2a) + (6b - 3b + b) |
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(3) + (3a - 2a) + (6b - 3b + b) |
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3 + a(3 - 2) + b(6 - 3+ 1) |
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3 + a(1) + b(4) |
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3 + a + 4b |
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