Question

Which answer describes the solution to each equation?

Column a
1. x-6/2 = x+13
2. 2+6x-7=8+2x-10+4x
3. 3x+5=1/5(15 x+10)
4. 1/4(16+8x)=3x-1-x+5
Column b
a. one solution
b. no solution
c. an infinite number of solutions

Answer 1

1. x-6/2 = x+13
multiply by 2 to eliminate fraction
2x - 6 = 2x + 26
-6 = 26
therefore has no solution.

2. 2+6x-7=8+2x-10+4x
2-7=8-10
therefore has no solution.


3. 3x+5=1/5(15 x+10)
5(15 x+10)(3x+5) = 1
(75x + 50)(3x + 5 ) = 1
225x^2 + 375x + 150x + 250 = 1
225x^2 + 525x + 249 = 0
this is a quadratic equation, that has 2 real solutions.

4. 1/4(16+8x)=3x-1-x+5
1 = (3x-1-x+5)4(16+8x)
1 = (2x + 4)4(16 + 8x)
1 = (8x + 16)(16 + 8x)
1 = (8x + 16)^2
1 = 64x^2 + 256x + 256
64x^2 + 256x + 255 = 0
this is a quadratic equation with two real solutions.