To solve the problem of combining like terms in the given expressions, we need to group and simplify the terms that have the same variable (e.g., all \(x\)-terms together) and constants (numbers without variables) together. Let's go through each expression step by step.
Expression 1: \(3x - 2x + 5x\)
- Combine the \(x\)-terms: \(3x - 2x + 5x = (3 - 2 + 5)x = 6x\)
- Result: \(6x\) (Option K)
Expression 2: \(4 + 2x - 5 + 2x\)
- Combine the \(x\)-terms: \(2x + 2x = 4x\)
- Combine the constants: \(4 - 5 = -1\)
- Result: \(4x - 1\) (Option M)
Expression 3: \(7x + 5 - 3x + 4\)
- Combine the \(x\)-terms: \(7x - 3x = 4x\)
- Combine the constants: \(5 + 4 = 9\)
- Result: \(4x + 9\) (Option D)
Expression 4: \(7 - 3x + 3 + 8x\)
- Combine the \(x\)-terms: \(-3x + 8x = 5x\)
- Combine the constants: \(7 + 3 = 10\)
- Result: \(5x + 10\) (Option F)
Expression 5: \(-2x + 11 + 6x\)
- Combine the \(x\)-terms: \(-2x + 6x = 4x\)
- Combine the constants: \(11\) (no other constants)
- Result: \(4x + 11\) (Option A)
Expression 6: \(-x + 12x\)
- Combine the \(x\)-terms: \(-x + 12x = 11x\)
- Result: \(11x\) (Option J)
Expression 7: \(-4x - 10x\)
- Combine the \(x\)-terms: \(-4x - 10x = -14x\)
- Result: \(-14x\) (Option E)
Expression 8: \(15x - 16x\)
- Combine the \(x\)-terms: \(15x - 16x = -x\)
- Result: \(-x\) (Option C)
Expression 9: \(5x - 15 - 20x + 10\)
- Combine the \(x\)-terms: \(5x - 20x = -15x\)
- Combine the constants: \(-15 + 10 = -5\)
- Result: \(-15x - 5\) (Option G)
Expression 10: \(-6 + 2x + 8\)
- Combine the \(x\)-terms: \(2x\) (no other \(x\)-terms)
- Combine the constants: \(-6 + 8 = 2\)
- Result: \(2x + 2\) (Option I)
Expression 11: \(6x - 2x + 8 + 4x + 9\)
- Combine the \(x\)-terms: \(6x - 2x + 4x = 8x\)
- Combine the constants: \(8 + 9 = 17\)
- Result: \(8x + 17\) (Option H)
Expression 12: \(x + 7 + 2x - 4 + 3x\)
- Combine the \(x\)-terms: \(x + 2x + 3x = 6x\)
- Combine the constants: \(7 - 4 = 3\)
- Result: \(6x + 3\) (Option N)
Expression 13: \(4x - x\)
- Combine the \(x\)-terms: \(4x - x = 3x\)
- Result: \(3x\) (Option O)
Expression 14: \(-8x + 9x\)
- Combine the \(x\)-terms: \(-8x + 9x = x\)
- Result: \(x\) (Option B)
Expression 15: \(-x - x\)
- Combine the \(x\)-terms: \(-x - x = -2x\)
- Result: \(-2x\) (Option L)
Final Matching:
1. \(3x - 2x + 5x\) →
K
2. \(4 + 2x - 5 + 2x\) →
M
3. \(7x + 5 - 3x + 4\) →
D
4. \(7 - 3x + 3 + 8x\) →
F
5. \(-2x + 11 + 6x\) →
A
6. \(-x + 12x\) →
J
7. \(-4x - 10x\) →
E
8. \(15x - 16x\) →
C
9. \(5x - 15 - 20x + 10\) →
G
10. \(-6 + 2x + 8\) →
I
11. \(6x - 2x + 8 + 4x + 9\) →
H
12. \(x + 7 + 2x - 4 + 3x\) →
N
13. \(4x - x\) →
O
14. \(-8x + 9x\) →
B
15. \(-x - x\) →
L
Final Answer:
\[
\boxed{K, M, D, F, A, J, E, C, G, I, H, N, O, B, L}
\]
Parent Tip: Review the logic above to help your child master the concept of 8th grade math worksheet printable.
