Question

PART I: Each of the cards on the top row has the same simplified expression as one of the cards. on the bottom row. Match the cards with equivalent expressions to complete the sentences

-4(5x-3)+12 -4(-6x+4) 10-2(4+12x) -2(-10x+3)
8x-3(-4x+2) -2(12x-1) -4(5x-6) 8-8(-3x+3)

1. Card A and Card _both simplify to_
2. Card B and Card _both simplify to_
3. Card C and Card _both simplify to_
4. Card D and Card both simelify to__

Answer 1

To find equivalent expressions, multiply the numbers in parentheses by the coefficients and simplify where possible. Then, match the cards with the same simplified expressions. Cards A and G, B and H, C and F, and D and E simplify to the same expressions respectively.

Step-by-step explanation:

To match the top row of cards with the bottom row based on equivalent expressions, we need to distribute the multiplication through the parentheses and simplify where possible. Following the mathematical rules that identical expressions must have the same value, let's start by simplifying each expression:

1. -4(5x-3)+12 simplifies to -20x + 12 + 12 which further simplifies to -20x + 24.
2. -4(-6x+4) simplifies to 24x - 16.
3. 10-2(4+12x) simplifies to 10 - 8 - 24x which further simplifies to -24x + 2.
4. -2(-10x+3) simplifies to 20x - 6.
5. 8x-3(-4x+2) simplifies to 8x + 12x - 6 which further simplifies to 20x - 6.
6. -2(12x-1) simplifies to -24x + 2.
7. -4(5x-6) simplifies to -20x + 24.
8. 8-8(-3x+3) simplifies to 8 + 24x - 24 which further simplifies to 24x - 16.

Now let's match the cards:

1. Card A (-4(5x-3)+12) and Card G (-4(5x-6)) both simplify to -20x + 24.
2. Card B (-4(-6x+4)) and Card H (8-8(-3x+3)) both simplify to 24x - 16.
3. Card C (10-2(4+12x)) and Card F (-2(12x-1)) both simplify to -24x + 2.
4. Card D (-2(-10x+3)) and Card E (8x-3(-4x+2)) both simplify to 20x - 6.

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