Question

1. \\(4( d - 17) + 3( 4d -12)\\)
2. \\(3( 20 x + 9) + (x - 16)\\)
3. \\((18 x - 25) - ( 13x - 25)\\)
4. \\(20 ( x - 3) - 6( x - 12)\\)
5. find the sum of \\((18 - 8x)\\) and \\((2x - 15)\\).
6. find the difference between \\(4(2v + 4)\\) and \\(3( 3v - 5)\\).

Explanation:

Problem 3

Step1: Distribute coefficients

$4(d-17) + 3(4d-12) = 4d - 68 + 12d - 36$

Step2: Combine like terms

$4d + 12d - 68 - 36 = 16d - 104$

Problem 4

Step1: Distribute coefficients

$3(20x+9) + (x-16) = 60x + 27 + x - 16$

Step2: Combine like terms

$60x + x + 27 - 16 = 61x + 11$

Problem 5

Step1: Remove parentheses

$(18x-25) - (13x-25) = 18x - 25 - 13x + 25$

Step2: Combine like terms

$18x - 13x - 25 + 25 = 5x$

Problem 6

Step1: Distribute coefficients

$20(x-3) - 6(x-12) = 20x - 60 - 6x + 72$

Step2: Combine like terms

$20x - 6x - 60 + 72 = 14x + 12$

Problem 7

Step1: Set up sum expression

$(18-8x) + (2x-15) = 18 - 8x + 2x - 15$

Step2: Combine like terms

$-8x + 2x + 18 - 15 = -6x + 3$

Problem 8

Step1: Set up difference expression

$4(2v+4) - 3(3v-5) = 8v + 16 - 9v + 15$

Step2: Combine like terms

$8v - 9v + 16 + 15 = -v + 31$

Answer:

1. $16d - 104$
2. $61x + 11$
3. $5x$
4. $14x + 12$
5. $-6x + 3$
6. $-v + 31$