To simplify these expressions, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. Constants (numbers without variables) are also considered like terms with each other.
Let's go through each expression one by one:
1.
2x + 1 + 3x - 6x + 2
- Combine the x terms: 2x + 3x - 6x = (2 + 3 - 6)x = -1x = -x
- Combine the constant terms: 1 + 2 = 3
- Result: -x + 3
2.
3y + 9 + 4y - 5
- Combine the y terms: 3y + 4y = 7y
- Combine the constant terms: 9 - 5 = 4
- Result: 7y + 4
3.
8 + 7x - 3x + 2 - 4
- Combine the x terms: 7x - 3x = 4x
- Combine the constant terms: 8 + 2 - 4 = 10 - 4 = 6
- Result: 4x + 6
4.
a + 2b + a - b
- Combine the a terms: a + a = 2a
- Combine the b terms: 2b - b = b
- Result: 2a + b
5.
2c + 6 - 7c + 7 + 3c + 2
- Combine the c terms: 2c - 7c + 3c = (2 - 7 + 3)c = -2c
- Combine the constant terms: 6 + 7 + 2 = 15
- Result: -2c + 15
6.
3d + 7 - 2d + 9 - 1
- Combine the d terms: 3d - 2d = d
- Combine the constant terms: 7 + 9 - 1 = 15
- Result: d + 15
7.
10y + 36 - 38y - 47
- Combine the y terms: 10y - 38y = -28y
- Combine the constant terms: 36 - 47 = -11
- Result: -28y - 11
8.
2 + 8x + 4 + 3x
- Combine the x terms: 8x + 3x = 11x
- Combine the constant terms: 2 + 4 = 6
- Result: 11x + 6
9.
8v + 6 - v + 6 + 2v + 3
- Combine the v terms: 8v - v + 2v = (8 - 1 + 2)v = 9v
- Combine the constant terms: 6 + 6 + 3 = 15
- Result: 9v + 15
10.
3u + 9 + 4u - 3
- Combine the u terms: 3u + 4u = 7u
- Combine the constant terms: 9 - 3 = 6
- Result: 7u + 6
11.
5s + 7 - 1 + 3s - s
- Combine the s terms: 5s + 3s - s = (5 + 3 - 1)s = 7s
- Combine the constant terms: 7 - 1 = 6
- Result: 7s + 6
12.
11q - 3q + 11 - 3 + q
- Combine the q terms: 11q - 3q + q = (11 - 3 + 1)q = 9q
- Combine the constant terms: 11 - 3 = 8
- Result: 9q + 8
Final Answer:
1. -x + 3
2. 7y + 4
3. 4x + 6
4. 2a + b
5. -2c + 15
6. d + 15
7. -28y - 11
8. 11x + 6
9. 9v + 15
10. 7u + 6
11. 7s + 6
12. 9q + 8
Parent Tip: Review the logic above to help your child master the concept of simplify worksheet.
