Question

Which of the following equations would have no solution?

A
−4+13x=13x−4

B
−2(x−2)=−3−2x

C
4x−40=7(−2x+2)

D
24x+12=12+24x

Answer 1

B

Explanation:

A

- 4 + 13x = 13x - 4

since both sides are the same then any value of x will make the equation true.

this equation has an infinite number of solutions

B

- 2(x - 2) = - 3 - 2x

- 2x + 4 = - 3 - 2x ( add 2x to both sides )

4 = - 3 ← not possible

this indicates the equation has no solutions

C

4x - 40 = 7(- 2x + 2)

4x - 40 = - 14x + 14 ( add 14x from both sides )

14x - 40 = 14 ( add 40 to both sides )

14x = 54 ( divide both sides by 14 )

x =
`(54)/(14)` =
`(27)/(7)` ← one solution

D

24x + 12 = 12 + 24x

since both sides are the same then any value of x will make the equation true.

this equation has an infinite number of solutions.