Sure, let's simplify each of the given expressions step by step.
### Expression 14:
[tex]\[ -3(4p - 7) + 8 \][/tex]
1. Distribute the -3:
[tex]\[ -12p + 21 \][/tex]
2. Combine the constants:
[tex]\[ -12p + 21 + 8 \][/tex]
[tex]\[ -12p + 29 \][/tex]
So, the simplified form is:
[tex]\[ -12p + 29 \][/tex]
---
### Expression 15:
[tex]\[ 4(x - 10) + 2(5x - 3) \][/tex]
1. Distribute the 4 and 2 respectively:
[tex]\[ 4x - 40 + 10x - 6 \][/tex]
2. Combine the like terms (4x and 10x, -40 and -6):
[tex]\[ 14x - 46 \][/tex]
So, the simplified form is:
[tex]\[ 14x - 46 \][/tex]
---
### Expression 17:
[tex]\[ -2(3r + 2s) + 3(4r - s) \][/tex]
1. Distribute the -2 and 3 respectively:
[tex]\[ -6r - 4s + 12r - 3s \][/tex]
2. Combine the like terms (-6r and 12r, -4s and -3s):
[tex]\[ ( -6r + 12r ) + ( -4s - 3s ) \][/tex]
[tex]\[ 6r - 7s \][/tex]
So, the simplified form is:
[tex]\[ 6r - 7s \][/tex]
---
### Expression 18:
[tex]\[ 2w - (5w + 6) \][/tex]
1. Distribute the negative sign inside the parenthesis:
[tex]\[ 2w - 5w - 6 \][/tex]
2. Combine the like terms (2w and -5w):
[tex]\[ -3w - 6 \][/tex]
So, the simplified form is:
[tex]\[ -3w - 6 \][/tex]
Thus, the simplified forms for each of the expressions are:
1. [tex]\( -12p + 29 \)[/tex]
2. [tex]\( 14x - 46 \)[/tex]
3. [tex]\( 6r - 7s \)[/tex]
4. [tex]\( -3w - 6 \)[/tex]
