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Analyzing Solutions

Question 5 • NC-Foundations of Math 1 (Fall) [1st 9 Weeks]

Which linear equations have one solution? Check all that apply.

Answer
A
5x – 1 = 3(x + 11)
B
4(x – 2) + 4x = 8(x – 9)
C
4(x – 6) + 4 = 2(x – 3)
D
2(x – 4) = 5(x – 3) + 3
E
2(x – 1) + 3x = 5(x – 2) + 3

Explanation

A linear equation has one solution when simplifying it gives a nonzero coefficient of x. In A, 5x − 1 = 3x + 33 simplifies to 2x = 34, so there is one solution. In C, 4x − 20 = 2x − 6 simplifies to 2x = 14, and in D, 2x − 8 = 5x − 12 simplifies to 3x = 4; both also have one solution. B is contradictory, while E simplifies to 5x − 2 = 5x − 2, which is true for every x.

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