Answer :
Let's combine like terms and simplify each expression step-by-step:
### Expression 6: \(3 k - 2 k + 12 + 5 r\)
1. Combine the terms involving \( k \):
[tex]\[3k - 2k = k\][/tex]
2. The remaining terms are \( 12 \) and \( 5 r \), which do not combine with any other terms in the expression.
Final simplified expression:
[tex]\[ k + 5r + 12 \][/tex]
### Expression 7: \(2 c + 3 b + 8 b + c\)
1. Combine the terms involving \( b \):
[tex]\[3b + 8b = 11b\][/tex]
2. Combine the terms involving \( c \):
[tex]\[2c + c = 3c\][/tex]
Final simplified expression:
[tex]\[ 11b + 3c \][/tex]
### Expression 8: \(5 k + 3 + 2 j - 2 - k\)
1. Combine the terms involving \( k \):
[tex]\[5k - k = 4k\][/tex]
2. Combine the constant terms:
[tex]\[3 - 2 = 1\][/tex]
3. The remaining term involving \( j \) does not combine with any others.
Final simplified expression:
[tex]\[ 4k + 2j + 1 \][/tex]
### Expression 9: \(7 + 4 p - 6 + 2 m - 2 p\)
1. Combine the terms involving \( p \):
[tex]\[4p - 2p = 2p\][/tex]
2. Combine the constant terms:
[tex]\[7 - 6 = 1\][/tex]
3. The remaining term involving \( m \) does not combine with any others.
Final simplified expression:
[tex]\[ 2p + 2m + 1 \][/tex]
### Expression 10: \(-4 n + 4 - (-2 d) + n - 5\)
1. Simplify \(-(-2d)\):
[tex]\[ \text{-(-2d) = 2d} \][/tex]
2. Combine terms involving \( n \):
[tex]\[-4n + n = -3n\][/tex]
3. Combine the constant terms:
[tex]\[4 - 5 = -1\][/tex]
Final simplified expression:
[tex]\[ 2d - 3n - 1 \][/tex]
### Expression 11: \(18 + (-4 x) + 1 - 3 x + 8 y\)
1. Combine the terms involving \( x \):
[tex]\[-4x - 3x = -7x\][/tex]
2. Combine the constant terms:
[tex]\[18 + 1 = 19\][/tex]
3. The remaining term involving \( y \) does not combine with any others.
Final simplified expression:
[tex]\[ -7x + 8y + 19 \][/tex]
### Expression 12: \(2 w + (-11) + 18 y + 2 w - 11\)
1. Combine the terms involving \( w \):
[tex]\[2w + 2w = 4w\][/tex]
2. Combine the constant terms:
[tex]\[-11 - 11 = -22\][/tex]
3. The remaining term involving \( y \) does not combine with any others.
Final simplified expression:
[tex]\[ 4w + 18y - 22 \][/tex]
### Expression 13: \(6 h - 12 - 9 h + 8 k + (-3 k)\)
1. Combine the terms involving \( h \):
[tex]\[6h - 9h = -3h\][/tex]
2. Combine the terms involving \( k \):
[tex]\[8k - 3k = 5k\][/tex]
3. The constant term \(-12\) does not combine with any others.
Final simplified expression:
[tex]\[ -3h + 5k - 12 \][/tex]
### Expression 14: \(3 - 3 m - 3 m - 8 p - 3 p\)
1. Combine the terms involving \( m \):
[tex]\[-3m - 3m = -6m\][/tex]
2. Combine the terms involving \( p \):
[tex]\[-8p - 3p = -11p\][/tex]
3. The constant term \(3\) does not combine with any others.
Final simplified expression:
[tex]\[ 3 - 6m - 11p \][/tex]
### Expression 15: \(14 x - 7 + 3 y - 7 x - 7 x\)
1. Combine the terms involving \( x \):
[tex]\[14x - 7x - 7x = 0x\][/tex]
[tex]\[14x -(7x +7x) = 0x\][/tex]
2. The term involving \( y \) does not combine with any other terms: \(3y\).
3. The constant term is \(-7\).
Final simplified expression:
[tex]\[ 3 y - 7 \][/tex]
Putting all the simplified answers together:
6. \( k + 5r + 12 \)
7. \( 11 b + 3 c \)
8. \( 4 k + 2 j + 1 \)
9. \( 2 p + 2 m + 1 \)
10. \( 2 d - 3 n - 1 \)
11. \( -7 x + 8 y + 19 \)
12. \( 4 w + 18 y - 22 \)
13. \( -3 h + 5 k - 12 \)
14. \( 3 - 6 m - 11 p \)
15. [tex]\( 3 y - 7\)[/tex]
### Expression 6: \(3 k - 2 k + 12 + 5 r\)
1. Combine the terms involving \( k \):
[tex]\[3k - 2k = k\][/tex]
2. The remaining terms are \( 12 \) and \( 5 r \), which do not combine with any other terms in the expression.
Final simplified expression:
[tex]\[ k + 5r + 12 \][/tex]
### Expression 7: \(2 c + 3 b + 8 b + c\)
1. Combine the terms involving \( b \):
[tex]\[3b + 8b = 11b\][/tex]
2. Combine the terms involving \( c \):
[tex]\[2c + c = 3c\][/tex]
Final simplified expression:
[tex]\[ 11b + 3c \][/tex]
### Expression 8: \(5 k + 3 + 2 j - 2 - k\)
1. Combine the terms involving \( k \):
[tex]\[5k - k = 4k\][/tex]
2. Combine the constant terms:
[tex]\[3 - 2 = 1\][/tex]
3. The remaining term involving \( j \) does not combine with any others.
Final simplified expression:
[tex]\[ 4k + 2j + 1 \][/tex]
### Expression 9: \(7 + 4 p - 6 + 2 m - 2 p\)
1. Combine the terms involving \( p \):
[tex]\[4p - 2p = 2p\][/tex]
2. Combine the constant terms:
[tex]\[7 - 6 = 1\][/tex]
3. The remaining term involving \( m \) does not combine with any others.
Final simplified expression:
[tex]\[ 2p + 2m + 1 \][/tex]
### Expression 10: \(-4 n + 4 - (-2 d) + n - 5\)
1. Simplify \(-(-2d)\):
[tex]\[ \text{-(-2d) = 2d} \][/tex]
2. Combine terms involving \( n \):
[tex]\[-4n + n = -3n\][/tex]
3. Combine the constant terms:
[tex]\[4 - 5 = -1\][/tex]
Final simplified expression:
[tex]\[ 2d - 3n - 1 \][/tex]
### Expression 11: \(18 + (-4 x) + 1 - 3 x + 8 y\)
1. Combine the terms involving \( x \):
[tex]\[-4x - 3x = -7x\][/tex]
2. Combine the constant terms:
[tex]\[18 + 1 = 19\][/tex]
3. The remaining term involving \( y \) does not combine with any others.
Final simplified expression:
[tex]\[ -7x + 8y + 19 \][/tex]
### Expression 12: \(2 w + (-11) + 18 y + 2 w - 11\)
1. Combine the terms involving \( w \):
[tex]\[2w + 2w = 4w\][/tex]
2. Combine the constant terms:
[tex]\[-11 - 11 = -22\][/tex]
3. The remaining term involving \( y \) does not combine with any others.
Final simplified expression:
[tex]\[ 4w + 18y - 22 \][/tex]
### Expression 13: \(6 h - 12 - 9 h + 8 k + (-3 k)\)
1. Combine the terms involving \( h \):
[tex]\[6h - 9h = -3h\][/tex]
2. Combine the terms involving \( k \):
[tex]\[8k - 3k = 5k\][/tex]
3. The constant term \(-12\) does not combine with any others.
Final simplified expression:
[tex]\[ -3h + 5k - 12 \][/tex]
### Expression 14: \(3 - 3 m - 3 m - 8 p - 3 p\)
1. Combine the terms involving \( m \):
[tex]\[-3m - 3m = -6m\][/tex]
2. Combine the terms involving \( p \):
[tex]\[-8p - 3p = -11p\][/tex]
3. The constant term \(3\) does not combine with any others.
Final simplified expression:
[tex]\[ 3 - 6m - 11p \][/tex]
### Expression 15: \(14 x - 7 + 3 y - 7 x - 7 x\)
1. Combine the terms involving \( x \):
[tex]\[14x - 7x - 7x = 0x\][/tex]
[tex]\[14x -(7x +7x) = 0x\][/tex]
2. The term involving \( y \) does not combine with any other terms: \(3y\).
3. The constant term is \(-7\).
Final simplified expression:
[tex]\[ 3 y - 7 \][/tex]
Putting all the simplified answers together:
6. \( k + 5r + 12 \)
7. \( 11 b + 3 c \)
8. \( 4 k + 2 j + 1 \)
9. \( 2 p + 2 m + 1 \)
10. \( 2 d - 3 n - 1 \)
11. \( -7 x + 8 y + 19 \)
12. \( 4 w + 18 y - 22 \)
13. \( -3 h + 5 k - 12 \)
14. \( 3 - 6 m - 11 p \)
15. [tex]\( 3 y - 7\)[/tex]
