Question

Choose all of the equations that have exactly one solution.A. 2(x - 4) = 0B. 7 + 3x = 11+xC. 5x - 8 = 7x + 4 - 2xD. 3 (2x - 1) = -3 + 6xE. 8x - 5 + 4x = 7x - 5-9

Answer 1

Solve each one for x:

A. 2(x - 4) = 0

Apply distributive property:

2(x)+2(-4)=0

2x-8=0

2x=8

x=8/2

x=4

A has one solution.

B.

7 + 3x = 11+x

3x-x =11-7

2x=4

x=4/2

x=2

B has one solution

C.

5x - 8 = 7x + 4 - 2x

5x-7x+2x = 4+8

0 = 12

C has no solution

D.

3 (2x - 1) = -3 + 6x

6x-3=-3+6x

6x-3 = 6x-3

D has infinite solutions

E.

8x - 5 + 4x = 7x - 5-9

8x+4x-7x=-5-9+5

5x = -9

x= -9/5

x=-1.8

E has one solution.

So, the equations that have only one solution are:

A,B, and E.