Let’s go through each problem one by one. We’ll combine like terms — that means we add or subtract the numbers with the same letter (variable) and also add or subtract the plain numbers (constants).
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1) 7a + 4 + 8
→ Combine constants: 4 + 8 = 12
→ Answer:
7a + 12
2) b + 5 + b + b
→ Combine b terms: b + b + b = 3b
→ Constants: 5
→ Answer:
3b + 5
3) 2c + 3 + c + 1
→ Combine c terms: 2c + c = 3c
→ Constants: 3 + 1 = 4
→ Answer:
3c + 4
4) d + 7 + d - 8
→ Combine d terms: d + d = 2d
→ Constants: 7 - 8 = -1
→ Answer:
2d - 1
5) 3e + 2 + 4e + 6
→ Combine e terms: 3e + 4e = 7e
→ Constants: 2 + 6 = 8
→ Answer:
7e + 8
6) 5 + 3f + 1 - f
→ Combine f terms: 3f - f = 2f
→ Constants: 5 + 1 = 6
→ Answer:
2f + 6
7) 3g - 5 - 2g + 2
→ Combine g terms: 3g - 2g = g
→ Constants: -5 + 2 = -3
→ Answer:
g - 3
8) 3 - 2h + 8 - h
→ Combine h terms: -2h - h = -3h
→ Constants: 3 + 8 = 11
→ Answer:
-3h + 11
9) 2i - 8 + 4i + 1
→ Combine i terms: 2i + 4i = 6i
→ Constants: -8 + 1 = -7
→ Answer:
6i - 7
10) 2j + k + 3j + 3k
→ Combine j terms: 2j + 3j = 5j
→ Combine k terms: k + 3k = 4k
→ Answer:
5j + 4k
11) 5l + 4 - 7l + 2
→ Combine l terms: 5l - 7l = -2l
→ Constants: 4 + 2 = 6
→ Answer:
-2l + 6
12) -4 + 5m - 5 - 3m
→ Combine m terms: 5m - 3m = 2m
→ Constants: -4 - 5 = -9
→ Answer:
2m - 9
13) 2n + 3o - 6n + 2o
→ Combine n terms: 2n - 6n = -4n
→ Combine o terms: 3o + 2o = 5o
→ Answer:
-4n + 5o
14) 10 - 7p - 8 + 3p
→ Combine p terms: -7p + 3p = -4p
→ Constants: 10 - 8 = 2
→ Answer:
-4p + 2
15) 4q - (2 + q)
→ First, distribute the minus sign: 4q - 2 - q
→ Combine q terms: 4q - q = 3q
→ Constant: -2
→ Answer:
3q - 2
16) (4 + 2r) + (7 - 6r)
→ Remove parentheses: 4 + 2r + 7 - 6r
→ Combine r terms: 2r - 6r = -4r
→ Constants: 4 + 7 = 11
→ Answer:
-4r + 11
17) (4 + 2s) - (7 - 6s)
→ Distribute the minus: 4 + 2s - 7 + 6s
→ Combine s terms: 2s + 6s = 8s
→ Constants: 4 - 7 = -3
→ Answer:
8s - 3
18) 9t - (6 - 4t)
→ Distribute the minus: 9t - 6 + 4t
→ Combine t terms: 9t + 4t = 13t
→ Constant: -6
→ Answer:
13t - 6
19) (4u + 7) - (5 + 7u)
→ Distribute the minus: 4u + 7 - 5 - 7u
→ Combine u terms: 4u - 7u = -3u
→ Constants: 7 - 5 = 2
→ Answer:
-3u + 2
20) 2v + 8w - (4w + 5v)
→ Distribute the minus: 2v + 8w - 4w - 5v
→ Combine v terms: 2v - 5v = -3v
→ Combine w terms: 8w - 4w = 4w
→ Answer:
-3v + 4w
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Final Answer:
1) 7a + 12
2) 3b + 5
3) 3c + 4
4) 2d - 1
5) 7e + 8
6) 2f + 6
7) g - 3
8) -3h + 11
9) 6i - 7
10) 5j + 4k
11) -2l + 6
12) 2m - 9
13) -4n + 5o
14) -4p + 2
15) 3q - 2
16) -4r + 11
17) 8s - 3
18) 13t - 6
19) -3u + 2
20) -3v + 4w
Parent Tip: Review the logic above to help your child master the concept of algebra for 6th grade worksheet.
