Answer :
Sure, let's simplify each expression step by step:
a) [tex]\(3z - 8z + 7z + 19z\)[/tex]:
1. Combine all the coefficients of [tex]\(z\)[/tex]: [tex]\(3 - 8 + 7 + 19\)[/tex].
2. Calculate: [tex]\(3 - 8 = -5\)[/tex]; [tex]\(-5 + 7 = 2\)[/tex]; [tex]\(2 + 19 = 21\)[/tex].
3. The simplified expression is [tex]\(21z\)[/tex].
b) [tex]\(2p + 5p - 4p - 6p + 7p\)[/tex]:
1. Combine all the coefficients of [tex]\(p\)[/tex]: [tex]\(2 + 5 - 4 - 6 + 7\)[/tex].
2. Calculate: [tex]\(2 + 5 = 7\)[/tex]; [tex]\(7 - 4 = 3\)[/tex]; [tex]\(3 - 6 = -3\)[/tex]; [tex]\(-3 + 7 = 4\)[/tex].
3. The simplified expression is [tex]\(4p\)[/tex].
d) [tex]\(4c - 6b - 2c + 12b\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(c\)[/tex]: [tex]\(4c - 2c\)[/tex].
- Terms with [tex]\(b\)[/tex]: [tex]\(-6b + 12b\)[/tex].
2. Simplify:
- [tex]\(4c - 2c = 2c\)[/tex].
- [tex]\(-6b + 12b = 6b\)[/tex].
3. The simplified expression is [tex]\(2c + 6b\)[/tex].
e) [tex]\(5f - 4u - 3f + 17f - 6u\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(f\)[/tex]: [tex]\(5f - 3f + 17f\)[/tex].
- Terms with [tex]\(u\)[/tex]: [tex]\(-4u - 6u\)[/tex].
2. Simplify:
- [tex]\(5f - 3f = 2f\)[/tex]; [tex]\(2f + 17f = 19f\)[/tex].
- [tex]\(-4u - 6u = -10u\)[/tex].
3. The simplified expression is [tex]\(19f - 10u\)[/tex].
g) [tex]\(7t - 4r - 2r + 6r - 3t\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(t\)[/tex]: [tex]\(7t - 3t\)[/tex].
- Terms with [tex]\(r\)[/tex]: [tex]\(-4r - 2r + 6r\)[/tex].
2. Simplify:
- [tex]\(7t - 3t = 4t\)[/tex].
- [tex]\(-4r - 2r = -6r\)[/tex]; [tex]\(-6r + 6r = 0\)[/tex].
3. The simplified expression is [tex]\(4t\)[/tex].
h) [tex]\(7d + 9g - 3g + 4d - 2g\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(d\)[/tex]: [tex]\(7d + 4d\)[/tex].
- Terms with [tex]\(g\)[/tex]: [tex]\(9g - 3g - 2g\)[/tex].
2. Simplify:
- [tex]\(7d + 4d = 11d\)[/tex].
- [tex]\(9g - 3g = 6g\)[/tex]; [tex]\(6g - 2g = 4g\)[/tex].
3. The simplified expression is [tex]\(11d + 4g\)[/tex].
j) [tex]\(3e + 5e - 7h - 12h - 4e\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(e\)[/tex]: [tex]\(3e + 5e - 4e\)[/tex].
- Terms with [tex]\(h\)[/tex]: [tex]\(-7h - 12h\)[/tex].
2. Simplify:
- [tex]\(3e + 5e = 8e\)[/tex]; [tex]\(8e - 4e = 4e\)[/tex].
- [tex]\(-7h - 12h = -19h\)[/tex].
3. The simplified expression is [tex]\(4e - 19h\)[/tex].
k) [tex]\(4u + 2s - 7s - 3s + 8u\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(u\)[/tex]: [tex]\(4u + 8u\)[/tex].
- Terms with [tex]\(s\)[/tex]: [tex]\(2s - 7s - 3s\)[/tex].
2. Simplify:
- [tex]\(4u + 8u = 12u\)[/tex].
- [tex]\(2s - 7s = -5s\)[/tex]; [tex]\(-5s - 3s = -8s\)[/tex].
3. The simplified expression is [tex]\(12u - 8s\)[/tex].
m) [tex]\(3c - 5v - 8c + 6g + 2v\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(c\)[/tex]: [tex]\(3c - 8c\)[/tex].
- Terms with [tex]\(v\)[/tex]: [tex]\(-5v + 2v\)[/tex].
2. Simplify:
- [tex]\(3c - 8c = -5c\)[/tex].
- [tex]\(-5v + 2v = -3v\)[/tex].
3. The simplified expression is [tex]\(-5c - 3v + 6g\)[/tex].
n) [tex]\(12h - 4s + 3h - 6t + 9s\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(h\)[/tex]: [tex]\(12h + 3h\)[/tex].
- Terms with [tex]\(s\)[/tex]: [tex]\(-4s + 9s\)[/tex].
2. Simplify:
- [tex]\(12h + 3h = 15h\)[/tex].
- [tex]\(-4s + 9s = 5s\)[/tex].
3. The simplified expression is [tex]\(15h + 5s - 6t\)[/tex].
p) [tex]\(4g - 8c - 2g - 5c + 6d\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(g\)[/tex]: [tex]\(4g - 2g\)[/tex].
- Terms with [tex]\(c\)[/tex]: [tex]\(-8c - 5c\)[/tex].
2. Simplify:
- [tex]\(4g - 2g = 2g\)[/tex].
- [tex]\(-8c - 5c = -13c\)[/tex].
3. The simplified expression is [tex]\(2g - 13c + 6d\)[/tex].
q) [tex]\(5s - 12t - 14t + 6h - 11s\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(s\)[/tex]: [tex]\(5s - 11s\)[/tex].
- Terms with [tex]\(t\)[/tex]: [tex]\(-12t - 14t\)[/tex].
2. Simplify:
- [tex]\(5s - 11s = -6s\)[/tex].
- [tex]\(-12t - 14t = -26t\)[/tex].
3. The simplified expression is [tex]\(-6s - 26t + 6h\)[/tex].
s) [tex]\(b + 5h + 3h - 17b - 6h + 7g\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(b\)[/tex]: [tex]\(b - 17b\)[/tex].
- Terms with [tex]\(h\)[/tex]: [tex]\(5h + 3h - 6h\)[/tex].
2. Simplify:
- [tex]\(b - 17b = -16b\)[/tex].
- [tex]\(5h + 3h = 8h\)[/tex]; [tex]\(8h - 6h = 2h\)[/tex].
3. The simplified expression is [tex]\(-16b + 2h + 7g\)[/tex].
t) [tex]\(2u - 4u + 7j + 4j - 6f - 5u\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(u\)[/tex]: [tex]\(2u - 4u - 5u\)[/tex].
- Terms with [tex]\(j\)[/tex]: [tex]\(7j + 4j\)[/tex].
2. Simplify:
- [tex]\(2u - 4u = -2u\)[/tex]; [tex]\(-2u - 5u = -7u\)[/tex].
- [tex]\(7j + 4j = 11j\)[/tex].
3. The simplified expression is [tex]\(-7u + 11j - 6f\)[/tex].
I hope this helps! Feel free to ask if you have any questions.
a) [tex]\(3z - 8z + 7z + 19z\)[/tex]:
1. Combine all the coefficients of [tex]\(z\)[/tex]: [tex]\(3 - 8 + 7 + 19\)[/tex].
2. Calculate: [tex]\(3 - 8 = -5\)[/tex]; [tex]\(-5 + 7 = 2\)[/tex]; [tex]\(2 + 19 = 21\)[/tex].
3. The simplified expression is [tex]\(21z\)[/tex].
b) [tex]\(2p + 5p - 4p - 6p + 7p\)[/tex]:
1. Combine all the coefficients of [tex]\(p\)[/tex]: [tex]\(2 + 5 - 4 - 6 + 7\)[/tex].
2. Calculate: [tex]\(2 + 5 = 7\)[/tex]; [tex]\(7 - 4 = 3\)[/tex]; [tex]\(3 - 6 = -3\)[/tex]; [tex]\(-3 + 7 = 4\)[/tex].
3. The simplified expression is [tex]\(4p\)[/tex].
d) [tex]\(4c - 6b - 2c + 12b\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(c\)[/tex]: [tex]\(4c - 2c\)[/tex].
- Terms with [tex]\(b\)[/tex]: [tex]\(-6b + 12b\)[/tex].
2. Simplify:
- [tex]\(4c - 2c = 2c\)[/tex].
- [tex]\(-6b + 12b = 6b\)[/tex].
3. The simplified expression is [tex]\(2c + 6b\)[/tex].
e) [tex]\(5f - 4u - 3f + 17f - 6u\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(f\)[/tex]: [tex]\(5f - 3f + 17f\)[/tex].
- Terms with [tex]\(u\)[/tex]: [tex]\(-4u - 6u\)[/tex].
2. Simplify:
- [tex]\(5f - 3f = 2f\)[/tex]; [tex]\(2f + 17f = 19f\)[/tex].
- [tex]\(-4u - 6u = -10u\)[/tex].
3. The simplified expression is [tex]\(19f - 10u\)[/tex].
g) [tex]\(7t - 4r - 2r + 6r - 3t\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(t\)[/tex]: [tex]\(7t - 3t\)[/tex].
- Terms with [tex]\(r\)[/tex]: [tex]\(-4r - 2r + 6r\)[/tex].
2. Simplify:
- [tex]\(7t - 3t = 4t\)[/tex].
- [tex]\(-4r - 2r = -6r\)[/tex]; [tex]\(-6r + 6r = 0\)[/tex].
3. The simplified expression is [tex]\(4t\)[/tex].
h) [tex]\(7d + 9g - 3g + 4d - 2g\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(d\)[/tex]: [tex]\(7d + 4d\)[/tex].
- Terms with [tex]\(g\)[/tex]: [tex]\(9g - 3g - 2g\)[/tex].
2. Simplify:
- [tex]\(7d + 4d = 11d\)[/tex].
- [tex]\(9g - 3g = 6g\)[/tex]; [tex]\(6g - 2g = 4g\)[/tex].
3. The simplified expression is [tex]\(11d + 4g\)[/tex].
j) [tex]\(3e + 5e - 7h - 12h - 4e\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(e\)[/tex]: [tex]\(3e + 5e - 4e\)[/tex].
- Terms with [tex]\(h\)[/tex]: [tex]\(-7h - 12h\)[/tex].
2. Simplify:
- [tex]\(3e + 5e = 8e\)[/tex]; [tex]\(8e - 4e = 4e\)[/tex].
- [tex]\(-7h - 12h = -19h\)[/tex].
3. The simplified expression is [tex]\(4e - 19h\)[/tex].
k) [tex]\(4u + 2s - 7s - 3s + 8u\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(u\)[/tex]: [tex]\(4u + 8u\)[/tex].
- Terms with [tex]\(s\)[/tex]: [tex]\(2s - 7s - 3s\)[/tex].
2. Simplify:
- [tex]\(4u + 8u = 12u\)[/tex].
- [tex]\(2s - 7s = -5s\)[/tex]; [tex]\(-5s - 3s = -8s\)[/tex].
3. The simplified expression is [tex]\(12u - 8s\)[/tex].
m) [tex]\(3c - 5v - 8c + 6g + 2v\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(c\)[/tex]: [tex]\(3c - 8c\)[/tex].
- Terms with [tex]\(v\)[/tex]: [tex]\(-5v + 2v\)[/tex].
2. Simplify:
- [tex]\(3c - 8c = -5c\)[/tex].
- [tex]\(-5v + 2v = -3v\)[/tex].
3. The simplified expression is [tex]\(-5c - 3v + 6g\)[/tex].
n) [tex]\(12h - 4s + 3h - 6t + 9s\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(h\)[/tex]: [tex]\(12h + 3h\)[/tex].
- Terms with [tex]\(s\)[/tex]: [tex]\(-4s + 9s\)[/tex].
2. Simplify:
- [tex]\(12h + 3h = 15h\)[/tex].
- [tex]\(-4s + 9s = 5s\)[/tex].
3. The simplified expression is [tex]\(15h + 5s - 6t\)[/tex].
p) [tex]\(4g - 8c - 2g - 5c + 6d\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(g\)[/tex]: [tex]\(4g - 2g\)[/tex].
- Terms with [tex]\(c\)[/tex]: [tex]\(-8c - 5c\)[/tex].
2. Simplify:
- [tex]\(4g - 2g = 2g\)[/tex].
- [tex]\(-8c - 5c = -13c\)[/tex].
3. The simplified expression is [tex]\(2g - 13c + 6d\)[/tex].
q) [tex]\(5s - 12t - 14t + 6h - 11s\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(s\)[/tex]: [tex]\(5s - 11s\)[/tex].
- Terms with [tex]\(t\)[/tex]: [tex]\(-12t - 14t\)[/tex].
2. Simplify:
- [tex]\(5s - 11s = -6s\)[/tex].
- [tex]\(-12t - 14t = -26t\)[/tex].
3. The simplified expression is [tex]\(-6s - 26t + 6h\)[/tex].
s) [tex]\(b + 5h + 3h - 17b - 6h + 7g\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(b\)[/tex]: [tex]\(b - 17b\)[/tex].
- Terms with [tex]\(h\)[/tex]: [tex]\(5h + 3h - 6h\)[/tex].
2. Simplify:
- [tex]\(b - 17b = -16b\)[/tex].
- [tex]\(5h + 3h = 8h\)[/tex]; [tex]\(8h - 6h = 2h\)[/tex].
3. The simplified expression is [tex]\(-16b + 2h + 7g\)[/tex].
t) [tex]\(2u - 4u + 7j + 4j - 6f - 5u\)[/tex]:
1. Group terms with the same variable:
- Terms with [tex]\(u\)[/tex]: [tex]\(2u - 4u - 5u\)[/tex].
- Terms with [tex]\(j\)[/tex]: [tex]\(7j + 4j\)[/tex].
2. Simplify:
- [tex]\(2u - 4u = -2u\)[/tex]; [tex]\(-2u - 5u = -7u\)[/tex].
- [tex]\(7j + 4j = 11j\)[/tex].
3. The simplified expression is [tex]\(-7u + 11j - 6f\)[/tex].
I hope this helps! Feel free to ask if you have any questions.
