Question

Which equation has exactly one solution?

A. -2x - 1 + 5x = 4 + 3x - 1
B. 2x - 3- X = 2 + 2x - 5
C. 6x + 2 - 4x = 4 + 2x - 8
D. 5x + 4x = 3(3x – 8)

Answer 1

B) 2x-3-x=2+2x-5 has exactly one solution.

Explanation:

A) -2x-1+5x=4+3x-1

-2x+5x-1=3x+3

3x-1=3x+3

3x-3x-1=3

0-1=3

-1=3

no solution

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B) 2x-3-x=2+2x-5

x-3=2x-3

x-2x-3=-3

-x-3=-3

-x=-3+3

-x=0

x=0

Has exactly one solution.

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C) 6x+2-4x=4+2x-8

2x+2=2x-4

2x-2x+2=-4

2=-4

no solution.

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D) 5x+4x=3(3x-8)

9x=3(3x-8)

3x=3x-8

3x-3x=8

0=8

no solution.

Answer 2

B

Explanation:

2x - 3 - x = 2 + 2x - 5

add like terms

x - 3 = -3 + 2x

subtract 2x to x on the other side

x - 3 = -3 + 2x

-2x - 2x

-x - 3 = -3

add 3 to the other side

-x - 3 = -3

+ 3 + 3

-x = 0

x = 0