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This answer key displays the correct sorting of linear equations into categories based on their number of solutions: one, none, or infinite.

Answer key for linear equations card sort showing equations sorted into one solution, no solution, and infinitely many solutions columns.

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Show Answer Key & Explanations Step-by-step solution for: Linear Equations: One Solution, No Solution, Infinitely Many ...

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Final Answer:
One solution:
5x + 11 = −4
6x + 2 = 14
18 = −2 + 4x
−9x − 3x = 2(x + 14)
3(x + 8) = 15x − 6 + 3x
12x − 15 = 8x − 3

No solution:
7x − 9 = 7x − 3
2(x + 8) = 2x + 8
4x + x = 8 + 5x
x + 5x − 11 = 2(3x + 5)
5(x + 4) = 5x − 18
4x − 16 = 4(x + 4)

Infinitely many solutions:
−18x = −2(9x)
4x = 5x − x
−10x + 4x = −6x
6(x − 2) = 3(2x − 4)
8x + 2x − 6 = 2(5x − 3)
2(4x + 7) = 13x − 5x + 14

Parent Tip: Review the logic above to help your child master the concept of one solution no solution infinite solutions worksheet.

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